Characterizations of snowflake metric spaces.
Characterizations of some bitopological separation axioms in terms of - closure operator
Characterizations of Some Classes of Perfect Spaces in Terms of Continuous Selections Avoiding Supporting Sets
Some kinds of perfect spaces, including paracompact perfectly normal spaces and collectionwise normal perfect spaces, are characterized in terms of continuous selections avoiding supporting sets. A necessary and sufficient condition on a domain space for a selection theorem of E. Michael [Fund. Math. 47 (1959), 173-178] to hold is also obtained.
Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. (Short Communication).
Characterizations of some near-continuous functions and near-open functions.
Characterizations of strongly compact spaces.
Characterizations of supercompact spaces
Characterizations of the countable infinite product of rationals and some related problems
Characterizations of uniformity-dependent dimension functions
Characterizations of Urysohn-closed spaces
Characterizations of -Lindelöf spaces
A topological space is said to be -Lindelöf [1] if every cover of by cozero sets of admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of -Lindelöf spaces.
Characterizations of -stratifiable spaces
Characterizations of σ-spaces
Characterizing cell-decomposable metrics.
Characterizing chainable, tree-like, and circle-like continua
We prove that a continuum X is tree-like (resp. circle-like, chainable) if and only if for each open cover 𝓤₄ = {U₁,U₂,U₃,U₄} of X there is a 𝓤₄-map f: X → Y onto a tree (resp. onto the circle, onto the interval). A continuum X is an acyclic curve if and only if for each open cover 𝓤₃ = {U₁,U₂,U₃} of X there is a 𝓤₃-map f: X → Y onto a tree (or the interval [0,1]).
Characterizing Hilbert space topology
Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂
It is shown that the hyperspace (resp. ) of non-empty closed (resp. closed and bounded) subsets of a metric space (X,d) is homeomorphic to ℓ₂ if and only if the completion X̅ of X is connected and locally connected, X is topologically complete and nowhere locally compact, and each subset (resp. each bounded subset) of X is totally bounded.
Characterizing plane ANR's by existence of local means
Characterizing polyhedrons and manifolds
In [5], W. Taylor shows that each particular compact polyhedron can be characterized in the class of all metrizable spaces containing an arc by means of first order properties of its clone of continuous operations. We will show that such a characterization is possible in the class of compact spaces and in the class of Hausdorff spaces containing an arc. Moreover, our characterization uses only the first order properties of the monoid of self-maps. Also, the possibility of characterizing the closed...
Characterizing realcompact spaces as limits of approximate polyhedral systems
Realcompact spaces can be characterized as limits of approximate inverse systems of Polish polyhedra.