Compact and extremally disconnected spaces.
Compact Hausdorff spaces with two open sets
Compact Hausdorff spaces with two or three types of open subspaces:new results and open questions
Compact minimalization of inverse systems
Compact objects surjectivity of epimorphisms and compactifications
Compact sets without converging sequences in the random real model.
Compact spaces homeomorphic to a ray of ordinals
Compact spaces that do not map onto finite products
We provide examples of nonseparable compact spaces with the property that any continuous image which is homeomorphic to a finite product of spaces has a maximal prescribed number of nonseparable factors.
Compact unions of closed subsets are closed and compact intersections of open subsets are open
Compacta are maximally -resolvable
It is well-known that compacta (i.e. compact Hausdorff spaces) are maximally resolvable, that is every compactum contains many pairwise disjoint dense subsets, where denotes the minimum size of a non-empty open set in . The aim of this note is to prove the following analogous result: Every compactum contains many pairwise disjoint -dense subsets, where denotes the minimum size of a non-empty set in .
Compactness and countable compactness in weak topologies
A bounded closed convex set K in a Banach space X is said to have quasi-normal structure if each bounded closed convex subset H of K for which diam(H) > 0 contains a point u for which ∥u-x∥ < diam(H) for each x ∈ H. It is shown that if the convex sets on the unit sphere in X satisfy this condition (which is much weaker than the assumption that convex sets on the unit sphere are separable), then relative to various weak topologies, the unit ball in X is compact whenever it is countably compact....
Compactness and extreme points of the set of quasi-measure extensions of a quasi-measure [Book]
Compactness as -pseudocompactness
Compactness in Metric Spaces
In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness,...
Compactness Notions in Fuzzy Neighborhood Spaces.
Compactness of the hyperplane topology
Compactness type properties in topological groups
Complete function spaces.
Completely regular proximities and RC-proximities
Complex Banach spaces with Valdivia dual unit ball.
We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.