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.
Concerning products of proximally fine uniform spaces
Concerning Splittability and Perfect Mappings
Concerning the shapes of n-dimensional spheres
Concerning two covering properties
Connected LCA groups are sequentially connected
We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if is a connected locally compact Abelian subgroup of a Hausdorff topological group and the quotient space is sequentially connected, then so is .
Construction functors for topological semigroups.
Continuous images and other topological properties of Valdivia compacta
We study topological properties of Valdivia compact spaces. We prove in particular that a compact Hausdorff space K is Corson provided each continuous image of K is a Valdivia compactum. This answers a question of M. Valdivia (1997). We also prove that the class of Valdivia compacta is stable with respect to arbitrary products and we give a generalization of the fact that Corson compacta are angelic.
Continuous images of which are homeomorphic to .
Contre-exemples associés aux théorèmes de Rosenthal. Quelques propriétés liées à ces résultats
Convergence in compacta and linear Lindelöfness
Let be a compact Hausdorff space with a point such that is linearly Lindelöf. Is then first countable at ? What if this is true for every in ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when is, in addition, -monolithic. We also prove that if is compact, Hausdorff, and is strongly discretely Lindelöf, for every in , then is first countable. An example of linearly Lindelöf...
Correction to the paper “A generalization of -compact spaces”