Some results on -spaces
We present several results related to -spaces where is a finite cardinal or ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.
Some set-theoretic constructions in topology
Some Set-Theoretical Aspects of Differentation Theory.
Some theorems about the embeddability of ANR-sets into decomposition spaces of
Space structures, their theory and application. II.
Spaced spaces
Spaces of ANR's
Spaces of ANR's. II
Spaces of continuous functions, -products and Box Topology
For a Tychonoff space , we will denote by the set of its isolated points and will be equal to . The symbol denotes the space of real-valued continuous functions defined on . is the Cartesian product with its box topology, and is with the topology inherited from . By we denote the set can be continuously extended to all of . A space is almost--resolvable if it can be partitioned by a countable family of subsets in such a way that every non-empty open subset of has a non-empty...
Spaces of order arcs in hyperspaces
Spaces of ω-limit sets of graph maps
Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.
Spaces with star countable extent
For a topological property , we say that a space is star if for every open cover of the space there exists such that . We consider space with star countable extent establishing the relations between the star countable extent property and the properties star Lindelöf and feebly Lindelöf. We describe some classes of spaces in which the star countable extent property is equivalent to either the Lindelöf property or separability. An example is given of a Tychonoff star Lindelöf space with...
Spaces with --linked topologies as special subspaces of separable spaces
We characterize spaces with --linked bases as specially embedded subspaces of separable spaces, and derive some corollaries, such as the -productivity of the property of having a -linked base.
Spectral structures and uniform continuity
Squares of Q sets
Striped structures of stable and unstable sets of expansive homeomorphisms and a theorem of K. Kuratowski on independent sets
We investigate striped structures of stable and unstable sets of expansive homeomorphisms and continuum-wise expansive homeomorphisms. The following theorem is proved: if f : X → X is an expansive homeomorphism of a compact metric space X with dim X > 0, then the decompositions and of X into stable and unstable sets of f respectively are uncountable, and moreover there is σ (= s or u) and ϱ > 0 such that there is a Cantor set C in X with the property that for each x ∈ C, contains a nondegenerate...
Strong shape of the Stone-Čech compactification
J. Keesling has shown that for connected spaces the natural inclusion of in its Stone-Čech compactification is a shape equivalence if and only if is pseudocompact. This paper establishes the analogous result for strong shape. Moreover, pseudocompact spaces are characterized as spaces which admit compact resolutions, which improves a result of I. Lončar.
Strongly sequential spaces.
Strongly sequential spaces
The problem of Y. Tanaka [10] of characterizing the topologies whose products with each first-countable space are sequential, is solved. The spaces that answer the problem are called strongly sequential spaces in analogy to strongly Fréchet spaces.
Strutture di convergenza per filtri