Compactification of the domains of certain rings of functions
Compactification-like extensions [Book]
Compactifications and -separation
Compactifications and uniformities on sigma frames
A bijective correspondence between strong inclusions and compactifications in the setting of -frames is presented. The category of uniform -frames is defined and a description of the Samuel compactification is given. It is shown that the Samuel compactification of a uniform frame is completely determined by the -frame consisting of its uniform cozero part, and consequently, any compactification of any frame is so determined.
Compactifications, and ring epimorphisms.
Compactifications de Bohr d'anneaux et de modules
Compactifications for some semigroups using the Whyburn construction.
Compactifications of convergence spaces.
Compactifications of fractal structures.
Compactifications of partially ordered sets
Compactifications with finite remainders
Compactifying a convergence space with functions.
Compactifying the space of homeomorphisms
Compactifying topologised semigroups.
Compact-like properties in hyperspaces
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.