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.

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.

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 .

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

Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.

2001 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 216, no 1, p. 17-22Article in journal (Refereed) Published

Abstract [en]

The existence of the Ginzburg-Landau vortex number is established for any configuration with finite action. As a consequence, Bogomol'nyi's formula for the critical action is valid for any finite action configuration.