×

zbMATH — the first resource for mathematics

Bitopological manifolds. (Russian) Zbl 0589.54042
A bitopological space is a pair (X,\(\beta)\), where X is a set, and \(\beta\) is a topological structure on \(X\times X\) which is called a bitopological structure. The bitopological structure \(\beta\) on a set X defines a topological structure on X which is denoted by \(\beta\) /X and is induced by diagonal imbedding \(j: X\to X\times X\), \(j(x)=(x,x)\), and \(\beta\) (as topological structure on \(X\times X)\). Let \(M=(X,\tau)\) be a topological manifold, and \(\beta\) is a bitopological structure on M such that \(\tau =\beta | X\). Then M is called a bitopological manifold. The paper represents an introduction to the theory of bitopological manifolds. It contains the basic definitions and results of the theory as well as some examples of bitopological manifolds.
Reviewer: A.K.Guc

MSC:
54E55 Bitopologies
57N99 Topological manifolds
PDF BibTeX XML Cite
Full Text: EuDML