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Tjatyrko, Vitalij
##### Publications (10 of 24) Show all publications
Tjatyrko, V. & Hattori, Y. (2016). On reversible and bijectively related topological spaces. Paper presented at International Conference on Topology and its Applications. Topology and its Applications, 201, 432-440
Open this publication in new window or tab >>On reversible and bijectively related topological spaces
2016 (English)In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 201, p. 432-440Article in journal (Refereed) Published
##### 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.

##### Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2016
##### Keywords
Continuous bijection; Reversible space; Bijectively related spaces; Sorgenfrey line; Khalimsky line
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-127047 (URN)10.1016/j.topol.2015.12.052 (DOI)000371936600034 ()
##### Conference
International Conference on Topology and its Applications
Available from: 2016-04-13 Created: 2016-04-13 Last updated: 2017-11-30
Tjatyrko, V. & Karassev, A. (2015). (Non)connectedness and (non)homogeneity. Topology and its Applications, 179, 122-130
Open this publication in new window or tab >>(Non)connectedness and (non)homogeneity
2015 (English)In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 179, p. 122-130Article in journal (Refereed) Published
##### 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.

Elsevier, 2015
##### Keywords
Homogeneous spaces; Local connectedness; Local contractibility; Components of path connectedness
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-113493 (URN)10.1016/j.topol.2014.08.022 (DOI)000346458900013 ()
##### Note

Funding Agencies|NSERC [257231-09]

Available from: 2015-01-19 Created: 2015-01-19 Last updated: 2017-12-05
Aigner, M., Tjatyrko, V. & Nyagahakwa, V. (2015). THE ALGEBRA OF SEMIGROUPS OF SETS. Mathematica Scandinavica, 116(2), 161-170
Open this publication in new window or tab >>THE ALGEBRA OF SEMIGROUPS OF SETS
2015 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 116, no 2, p. 161-170Article in journal (Refereed) Published
##### 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.

##### Place, publisher, year, edition, pages
MATEMATISK INST, 2015
##### National Category
Algebra and Logic
##### Identifiers
urn:nbn:se:liu:diva-120758 (URN)000358751500001 ()
Available from: 2015-08-24 Created: 2015-08-24 Last updated: 2017-12-04
Tjatyrko, V. A. & Hattori, Y. (2013). A poset of topologies on the set of real numbers. Commentationes Mathematicae Universitatis Carolinae, 54(2), 189-196
Open this publication in new window or tab >>A poset of topologies on the set of real numbers
2013 (English)In: Commentationes Mathematicae Universitatis Carolinae, ISSN 0010-2628, E-ISSN 1213-7243, Vol. 54, no 2, p. 189-196Article in journal (Refereed) Published
##### 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 $(\mathbb R, \tau(A)), A\subseteq \mathbb R$.

##### Keywords
Sorgenfrey line; poset of topologies on the set of real numbers
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-108328 (URN)
Available from: 2014-06-26 Created: 2014-06-26 Last updated: 2017-12-05Bibliographically approved
Aigner, M., Tjatyrko, V. A. & Nyagahakwa, V. (2013). ON COUNTABLE FAMILIES OF SETS WITHOUT THE BAIRE PROPERTY. Colloquium Mathematicum, 133(2), 179-187
Open this publication in new window or tab >>ON COUNTABLE FAMILIES OF SETS WITHOUT THE BAIRE PROPERTY
2013 (English)In: Colloquium Mathematicum, ISSN 0010-1354, E-ISSN 1730-6302, Vol. 133, no 2, p. 179-187Article in journal (Refereed) Published
##### 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.

##### Place, publisher, year, edition, pages
Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics), 2013
##### Keywords
Vitali set; Baire property; admissible extension of a topology
Natural Sciences
##### Identifiers
urn:nbn:se:liu:diva-103315 (URN)10.4064/cm133-2-4 (DOI)000328741300004 ()
Available from: 2014-01-16 Created: 2014-01-16 Last updated: 2017-12-06
Chatyrko, V. A. & Karassev, A. (2013). On metrizable remainders of locally compact separable metrizable  spaces. Houston Journal of Mathematics, 39(3), 1067-1081
Open this publication in new window or tab >>On metrizable remainders of locally compact separable metrizable  spaces
2013 (English)In: Houston Journal of Mathematics, ISSN 0362-1588, Vol. 39, no 3, p. 1067-1081Article in journal (Refereed) Published
##### 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).

##### Place, publisher, year, edition, pages
University of Houston, Department of Mathematics, 2013
##### Keywords
Locally compact space, separable metrizable space, metrizable compactification, metrizable remainder
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-102414 (URN)000326961200019 ()
##### Note

Funding Agencies|NSERC|257231-04|

Available from: 2013-12-09 Created: 2013-12-09 Last updated: 2017-12-06Bibliographically approved
Tjatyrko, V. A. & Hattori, Y. (2013). Small Scattered Topological Invariants. Matematychni Studii, 39(2), 212-222
Open this publication in new window or tab >>Small Scattered Topological Invariants
2013 (English)In: Matematychni Studii, ISSN 1027-4634, Vol. 39, no 2, p. 212-222Article in journal (Refereed) Published
##### 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.

##### Keywords
small transfinite inductive dimension, separation dimension, countable-dimensional spaces, σ -hereditarily disconnected spaces
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-108329 (URN)
Available from: 2014-06-26 Created: 2014-06-26 Last updated: 2014-08-25Bibliographically approved
Tjatyrko, V. A. & Karassev, A. (2013). The (dis)connectedness of products in the box topology. Questions & Answers in General Topology, 31(1), 11-21
Open this publication in new window or tab >>The (dis)connectedness of products in the box topology
2013 (English)In: Questions & Answers in General Topology, ISSN 0918-4732, Vol. 31, no 1, p. 11-21Article in journal (Refereed) Published
##### 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.

Mathematics
##### Identifiers
urn:nbn:se:liu:diva-108330 (URN)
Available from: 2014-06-26 Created: 2014-06-26 Last updated: 2014-08-25
Chatyrko (Tjatyrko), V. A. & Hattori, Y. (2008). Addition and product theorems for ind. Topology and its Applications, 155(17-18), 2202-2210
Open this publication in new window or tab >>Addition and product theorems for ind
2008 (English)In: Topology and its Applications, ISSN 0166-8641, E-ISSN 1879-3207, Vol. 155, no 17-18, p. 2202-2210Article in journal (Refereed) Published
##### 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].

##### Place, publisher, year, edition, pages
Elsevier Science B.V., Amsterdam., 2008
##### Keywords
Regular spaces; Small inductive dimension
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-59818 (URN)10.1016/j.topol.2007.05.028 (DOI)260411400036 ()
Available from: 2010-09-25 Created: 2010-09-24 Last updated: 2017-12-12
Tjatyrko, V. & Hattori, Y. (2008). Infinite-dimensionality modulo absolute Borel classes. Bulletin of the Polish Academy of Sciences. Mathematics, 56(2), 163-176
Open this publication in new window or tab >>Infinite-dimensionality modulo absolute Borel classes
2008 (English)In: Bulletin of the Polish Academy of Sciences. Mathematics, ISSN 0239-7269, Vol. 56, no 2, p. 163-176Article in journal (Refereed) Published
Mathematics
##### Identifiers
urn:nbn:se:liu:diva-44670 (URN)77263 (Local ID)77263 (Archive number)77263 (OAI)
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-10

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