-spaces and -sets
-point finite refinable spaces.
Samuel compactification and uniform coreflection of nearness -frames
We introduce the structure of a nearness on a -frame and construct the coreflection of the category of nearness -frames to the category of compact regular -frames. This description of the Samuel compactification of a nearness -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform -frames in [11]. We also construct the uniform coreflection of a nearness -frame, that is, the coreflection of the category of to the category...
Scattered compactification for the Arens’ space
Scattered compactifications
Seeking a network characterization of Corson compacta
We say that a collection of subsets of has property if there is a set and point-countable collections of closed subsets of such that for any there is a finite subcollection of such that . Then we prove that any compact space is Corson if and only if it has a point-- base. A characterization of Corson compacta in terms of (strong) point network is also given. This provides an answer to an open question in “A Biased View of Topology as a Tool in Functional Analysis” (2014) by...
Selection principles and Baire spaces
Selection principles and upper semicontinuous functions
In connection with a conjecture of Scheepers, Bukovský introduced properties wQN* and SSP* and asked whether wQN* implies SSP*. We prove it in this paper. We also give characterizations of properties S₁(Γ,Ω) and in terms of upper semicontinuous functions
Semi separation axioms and hyperspaces.
Semialgebraic Topology Over a Real Closed Field I: Paths and Components in the Set of Rational Points of an Algebraic Variety.
Semialgebraic Topology over a Real Closed Field II: Basic Theory of Semialgebraic Spaces.
Semicompactness in fuzzy topological spaces.
Semiconvex compacta
We define and investigate a generalization of the notion of convex compacta. Namely, for semiconvex combination in a semiconvex compactum we allow the existence of non-trivial loops connecting a point with itself. It is proved that any semiconvex compactum contains two non-empty convex compacta, the center and the weak center. The center is the largest compactum such that semiconvex combination induces a convex structure on it. The convex structure on the weak center does not necessarily coincide...
Semi-generalized continuous maps in topological spaces.
Semigroup structure in compactifications of ordered semigroups
Semigroupes semitopologiques compacts admettant un sous-groupe dense.
Semigroups and their one-point compactifications.
Semilocal connectedness of product spaces and -continuity of maps.
Semi-precontinuous functions and properties of generalized semi-preclosed sets in topological spaces.
Semi-radiality in products.