Compact spaces and products of finite spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Products of Nearly Compact Spaces

Products of sequential CLP-compact spaces are CLP-compact

It is shown that the product of finitely many sequential, CLP-compact spaces is CLPcompact. The class of spaces which have the property that every cover by clopen sets — sets which are both open and closed — has a finite subcover was introduced by A. Šostak in [1] under the name CBcompact. These spaces are now known as CLP-compact spaces and their study is linked to the question of whether the ...

Compact Factors in Finally Compact Products of Topological Spaces

We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...

Countable Products of Spaces of Finite Sets

σn(Γ) = {x ∈ {0, 1} Γ : |supp(x)| ≤ n}. Here supp(x) = {γ ∈ Γ : xγ 6= 0}. This is a closed, hence compact subset of {0, 1}, which is identified with the family of all subsets of Γ of cardinality at most n. In this work we will study the spaces which are countable products of spaces σn(Γ), mainly their topological classification as well as the classification of their Banach spaces of continuous ...