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  • 1.
    Aigner, Mats
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Tjatyrko, Vitalij
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Nyagahakwa, Venuste
    National University of Rwanda, Rwanda .
    ON COUNTABLE FAMILIES OF SETS WITHOUT THE BAIRE PROPERTY2013In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 133, no 2, p. 179-187Article in journal (Refereed)
    Abstract [en]

    We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (R-n , tau), where n is an integer greater than= 1 and tau is any admissible extension of the Euclidean topology of R-n (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family F of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of F does not have the Baire property in X.

  • 2.
    Aigner, Mats
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Tjatyrko, Vitalij
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Nyagahakwa, Venuste
    National University of Rwanda, Rwanda.
    THE ALGEBRA OF SEMIGROUPS OF SETS2015In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 116, no 2, p. 161-170Article in journal (Refereed)
    Abstract [en]

    We study the algebra of semigroups of sets (i.e. families of sets closed under finite unions) and its applications. For each n greater than 1 we produce two finite nested families of pairwise different semigroups of sets consisting of subsets of R" without the Baire property.

  • 3. Charalambous, Michael G.
    et al.
    Tjatyrko, Vitalij
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Some estimates of the inductive dimensions of the union of two sets2005In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 146-147, p. 227-238Article in journal (Refereed)
    Abstract [en]

    We obtain estimates of the small and large inductive dimensions ind and Ind of the union of two sets, outside the class of completely normal spaces. We show that, in the sense of the inductive dimensions ind0 and Ind0 introduced independently by Charalambous and Filippov, a compact completely normal space which is the union of two dense zero-dimensional subspaces can be infinite-dimensional. © 2004 Elsevier B.V. All rights reserved.

  • 4.
    Chatyrko (Tjatyrko), Vitalij A
    et al.
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Hattori, Yasunao
    Shimane University.
    Addition and product theorems for ind2008In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 155, no 17-18, p. 2202-2210Article in journal (Refereed)
    Abstract [en]

    In this paper we improve two theorems for the small inductive dimension ind in the regular T-1-spaces: an addition theorem from [M.G Charalambous, V.A. Chatyrko. Some estimates of the inductive dimensions of the union of two sets, Topology Appl. 146/147 (2005) 227-238] and a product theorem from [V.A. Chatyrko. K.L. Kozlov. On (transfinite) small inductive dimension of products. Comment. Math. Univ. Carolin. 41 (3) (2000) 597-603].

  • 5.
    Chatyrko, Vitalij A.
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Karassev, Alexandre
    Nipissing University, North Bay, ON, Canada .
    On metrizable remainders of locally compact separable metrizable  spaces2013In: Houston Journal of Mathematics, ISSN 0362-1588, Vol. 39, no 3, p. 1067-1081Article in journal (Refereed)
    Abstract [en]

    In this paper we describe those locally compact noncompact separable metrizable spaces X for which the class R(X) of all metrizable remainders of X consists of all metrizable non-empty compacta. Then we show that for any pair X and X of locally compact noncompact connected separable metrizable spaces, either R(X) subset of R(X) or R(X) subset of R(X).

  • 6.
    Chatyrko, Vitalij
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Han, Sang-Eon
    Chonbuk National University, South Korea .
    Hattori, Yasunao
    Shimane University, Japan .
    Some Remarks Concerning Semi-T-1/2 Spaces2014In: Filomat, ISSN 0354-5180, Vol. 28, no 1, p. 21-25Article in journal (Refereed)
    Abstract [en]

    In this paper we prove that each subspace of an Alexandroff T-0-space is semi-T-1/2. In particular, any subspace of the folder X-n, where n is a positive integer and X is either the Khalimsky line (Z,tau(K)), the Marcus-Wyse plane (Z(2), tau(MW)) or any partially ordered set with the upper topology is semi-T-1/2. Then we study the basic properties of spaces possessing the axiom semi-T-1/2 such as finite productiveness and monotonicity.

  • 7.
    Chatyrko, Vitalij
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Karassev, Alexandre
    Nipissing University, Ontario, Canada.
    Reversible spaces and products2017In: Topology Proceedings, ISSN 0146-4124, E-ISSN 2331-1290, Vol. 49, p. 317-320Article in journal (Refereed)
    Abstract [en]

    A topological space is reversible if every continuous bijection f:X→X is a homeomorphism. There are many examples of reversiblespaces; in particular, Hausdorff compact spaces and locally Euclidean spaces are such. Chatyrko and Hattori observed, in a manuscript, that any product of topological spaces is non-reversible whenever at least one of the spaces is non-reversible and asked whether the topological product of two connected reversible spaces is reversible. The authors prove here that there are connected reversible spaces such that their product is not reversible. In fact, they construct a reversible space X which is a connected 2-manifold in R3 without boundary such that X×[0,1] is not reversible.

  • 8. Fedorchuk, V V
    et al.
    Tjatyrko, Vitalij
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On the Brouwer dimension of one-dimensional compact Hausdorff spaces.2005In: Vestnik Moskovskogo universiteta. Seriâ 1, Matematika, mehanika, ISSN 0579-9368, Vol. 2, p. 22-27Article in journal (Refereed)
  • 9.
    Tjatyrko, Vitalij
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On inductive compactness degree2004In: Geometric Topology: Infinite-Dimensional Topology, Absolut Extensors, Applications,2004, 2004Conference paper (Other academic)
  • 10.
    Tjatyrko, Vitalij
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On the relationship between cmp and def for separable metrizable spaces2005In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 152, no 3 SPEC. ISS., p. 269-274Article in journal (Refereed)
    Abstract [en]

    For each pair of positive integers k and m with k ≤ m there exists a separable metrizable space X (k, m) such that cmp X (k, m) = k and def X (k, m) = m. This solves Problem 6 from [J.M. Aarts, T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993, p. 71]. © 2004 Elsevier B.V. All rights reserved.

  • 11.
    Tjatyrko, Vitalij
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    On the relationship between cmp and def in the class of separable metrizable spaces2003In: V Iberoamerican Conference on General Topology and its Applications,2003, 2003Conference paper (Other academic)
  • 12.
    Tjatyrko, Vitalij
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Subspaces of the Sorgenfrey line and their products2006In: Tsukuba journal of mathematics, ISSN 0387-4982, Vol. 30, no 2, p. 401-414Article in journal (Refereed)
  • 13.
    Tjatyrko, Vitalij A.
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Hattori, Yasunao
    Department of Mathematics, Shimane University, Matsue, Japan.
    A poset of topologies on the set of real numbers2013In: Commentationes Mathematicae Universitatis Carolinae, ISSN 0010-2628, E-ISSN 1213-7243, Vol. 54, no 2, p. 189-196Article in journal (Refereed)
    Abstract [en]

    On the set $\mathbb R$ of real numbers we consider a poset $\mathcal P_\tau(\mathbb R)$ (by inclusion) of topologies $\tau(A)$, where $A\subseteq \mathbb R$, such that $A_1\supseteq A_2$ iff $\tau(A_1)\subseteq \tau(A_2)$. The poset has the minimal element $\tau (\mathbb R)$, the Euclidean topology, and the maximal element $\tau (\emptyset)$, the Sorgenfrey topology. We are interested when two topologies $\tau_1$ and $\tau_2$ (especially, for $\tau_2 = \tau(\emptyset)$) from the poset define homeomorphic spaces $(\mathbb R, \tau_1)$ and $(\mathbb R, \tau_2)$. In particular, we prove that for a closed subset $A$ of $\mathbb R$ the space $(\mathbb R, \tau(A))$ is homeomorphic to the Sorgenfrey line $(\mathbb R, \tau(\emptyset))$ iff $A$ is countable. We study also common properties of the spaces $(\mathbb R, \tau(A)), A\subseteq \mathbb R$.

  • 14.
    Tjatyrko, Vitalij A.
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Hattori, Yasunao
    Department of Mathematics, Shimane University, Matsue, Japan.
    Small Scattered Topological Invariants2013In: Matematychni Studii, ISSN 1027-4634, Vol. 39, no 2, p. 212-222Article in journal (Refereed)
    Abstract [en]

    We present a unified approach to define dimension functions like trind, trindp, trt and p. We show how some similar facts on these functions can be proved similarly. Moreover, several new classes of infinite-dimensional spaces close to the classes of countable-dimensional and σ-hereditarily disconnected ones are introduced. We prove a compactification theorem for these classes.

  • 15.
    Tjatyrko, Vitalij A.
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Karassev, Alexandre
    Nipissing University, North Bay, ON, Canada.
    The (dis)connectedness of products in the box topology2013In: Questions & Answers in General Topology, ISSN 0918-4732, Vol. 31, no 1, p. 11-21Article in journal (Refereed)
    Abstract [en]

    We suggest two independent sufficient conditions on topological connected spaces with axioms lower than $T_3$, which imply disconnectedness, and one sufficient condition, which implies connectedness, of products of spaces endowed with the box topology.

  • 16.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Charalambous, M. G.
    Notes on the inductive dimension Ind02003In: Topology Proceedings, ISSN 0146-4124, E-ISSN 2331-1290, Vol. 27, no 2, p. 395-410Article in journal (Refereed)
  • 17.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Charalambous, M. G.
    Hattori, Y.
    The behaviour of (transfinite) dimension functions on unions of closed subsets2004In: Journal of the Mathematical Society of Japan, ISSN 0025-5645, E-ISSN 1881-1167, Vol. 56, no 2, p. 489-501Article in journal (Refereed)
  • 18.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Fedorchuk, Vitaly V
    Dimensionsgrad for nonmetrizable compact spaces2003Report (Other academic)
  • 19.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Hattori, Y.
    Around the equality ind X = Ind X towards to a unifying theorem2003In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 131, p. 295-302Article in journal (Refereed)
  • 20.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Hattori, Y.
    Ohta, H.
    On representation of spaces by unions of locally compact subspaces2004In: III Japan-Mexico Joint Meeting on Topology and its Applications,2004, 2004Conference paper (Other academic)
  • 21.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Hattori, Y.
    Ohta, H.
    Partitions of spaces by locally compact subspaces2006In: Houston Journal of Mathematics, ISSN 0362-1588, Vol. 32, no 4, p. 1077-1091Article in journal (Refereed)
    Abstract [en]

    In this article, we shall discuss the possibility of different presentations of (locally compact) spaces as unions or partitions of locally compact subspaces. © 2006 University of Houston.

  • 22.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Hattori, Yasunao
    Infinite-dimensionality modulo absolute Borel classes2008In: Bulletin of the Polish Academy of Sciences. Mathematics, ISSN 0239-7269, Vol. 56, no 2, p. 163-176Article in journal (Refereed)
  • 23.
    Tjatyrko, Vitalij
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Hattori, Yasunao
    Shimane University, Japan.
    On reversible and bijectively related topological spaces2016In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 201, p. 432-440Article in journal (Refereed)
    Abstract [en]

    We consider the following classical problems: (1) For what spaces X and Y the existence of continuous bijections of X onto Y and Y onto X implies or does not imply that the spaces are homeomorphic? (2) For what spaces X is each continuous bijection of X onto itself a homeomorphism? Some answers to the questions are suggested. (C) 2015 Elsevier B.V. All rights reserved.

  • 24.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Hattori, Yasunao
    There is no upper bound of small transfinite compactness degree in metrizable spaces2007In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 154, no 7, p. 1314-1320Article in journal (Refereed)
  • 25.
    Tjatyrko, Vitalij
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Karassev, Alexandre
    Nipissing University, Canada.
    (Non)connectedness and (non)homogeneity2015In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 179, p. 122-130Article in journal (Refereed)
    Abstract [en]

    We discuss an approach to a problem posed by A.V. Arhangelskii and E.K. van Douwen on a possibility to present a compact space as a continuous image of a homogeneous compact space. Then we suggest some ways of proving nonhomogeneity of tau-powers of a space X using points of local connectedness (or local contractibility) and components of path connectedness of X.

  • 26.
    Tjatyrko, Vitalij
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Zarichnyi, M.
    A remark on asymptotic dimension and digital dimension of finite metric spaces2007In: Matematychni Studii, ISSN 1027-4634, Vol. 27, no 1, p. 100-104Article in journal (Refereed)
1 - 26 of 26
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