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Start Over Descriptor "54A10" Journal central european journal of mathematics
5 results on '"54A10"'

1. On similarity between topologies.

Author

Bartoszewicz, Artur, Filipczak, Małgorzata, Kowalski, Andrzej, and Terepeta, Małgorzata

Abstract

Let T and T be topologies defined on the same set X and let us say that ( X, T) and ( X, T) are similar if the families of sets which have nonempty interior with respect to T and T coincide. The aim of the paper is to study how similar topologies are related with each other. [ABSTRACT FROM AUTHOR]

Published
2014
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2. On the structure of perfect sets in various topologies associated with tree forcings.

Author

Nowik, Andrzej and Reardon, Patrick

Abstract

We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above. [ABSTRACT FROM AUTHOR]

Published
2013
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3. A category Ψ-density topology

Author

Wojciech Wojdowski and Władysław Wilczyński

Subjects
Discrete mathematics, density point, General Mathematics, density topology, Lebesgue's number lemma, 54a10, Initial topology, Lebesgue integration, Topology, symbols.namesake, Number theory, QA1-939, symbols, Point (geometry), Particular point topology, Representation (mathematics), 28a05, Mathematics, Topology (chemistry)
Abstract

Ψ-density point of a Lebesgue measurable set was introduced by Taylor in [Taylor S.J., On strengthening the Lebesgue Density Theorem, Fund. Math., 1958, 46, 305–315] and [Taylor S.J., An alternative form of Egoroff’s theorem, Fund. Math., 1960, 48, 169–174] as an answer to a problem posed by Ulam. We present a category analogue of the notion and of the Ψ-density topology. We define a category analogue of the Ψ-density point of the set A at a point x as the Ψ-density point at x of the regular open representation of A.

Published
2011

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