Compactness and product spaces

Relative Compactness and Product Stable Quotient Maps

Function spaces and compactness

It is useful to treat real-valued functions (or complex-valued functions, or vector space-valued functions) as elements of a vector space, so that the tools from linear algebra can be applied. Given a set X one may consider the vector space R of all real-valued functions with domain X. If X is finite, say with n elements, then this is just the familiar vector space R. The more interesting examp...

Compactness in apartness spaces?

In this note, we establish some results which suggest a possible solution to the problem of finding the right constructive notion of compactness in the context of a not–necessarily–uniform apartness space.

Compactness of Loeb Spaces

In this paper we show that the compactness of a Loeb space depends on its cardinality, the nonstandard universe it belongs to and the underlying model of set theory we live in. In §1 we prove that Loeb spaces are compact under various assumptions, and in §2 we prove that Loeb spaces are not compact under various other assumptions. The results in §1 and §2 give a quite complete answer to a quest...

Semi compactness and semi-I-compactness in ditopological texture spaces

In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].