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On Q -algebras.

Neggers, Joseph, Ahn, Sun Shin, Kim, Hee Sik (2001)

International Journal of Mathematics and Mathematical Sciences

On quasi-uniform space valued semi-continuous functions

Tomasz Kubiak, María Angeles de Prada Vicente (2009)

Commentationes Mathematicae Universitatis Carolinae

F. van Gool [Comment. Math. Univ. Carolin. 33 (1992), 505–523] has introduced the concept of lower semicontinuity for functions with values in a quasi-uniform space ( R , 𝒰 ) . This note provides a purely topological view at the basic ideas of van Gool. The lower semicontinuity of van Gool appears to be just the continuity with respect to the topology T ( 𝒰 ) generated by the quasi-uniformity 𝒰 , so that many of his preparatory results become consequences of standard topological facts. In particular, when the order...

On reflexive closed set lattices

Zhongqiang Yang, Dong Sheng Zhao (2010)

Commentationes Mathematicae Universitatis Carolinae

For a topological space X , let S ( X ) denote the set of all closed subsets in X , and let C ( X ) denote the set of all continuous maps f : X X . A family 𝒜 S ( X ) is called reflexive if there exists 𝒞 C ( X ) such that 𝒜 = { A S ( X ) : f ( A ) A for every f 𝒞 } . Every reflexive family of closed sets in space X forms a sub complete lattice of the lattice of all closed sets in X . In this paper, we continue to study the reflexive families of closed sets in various types of topological spaces. More necessary and sufficient conditions for certain families of closed...

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