Coshape-invariant functors and Mackey's induced representation theorem
Countable compactness of lexicographic products of GO-spaces
We characterize the countable compactness of lexicographic products of GO-spaces. Applying this characterization about lexicographic products, we see:
Countable decomposition of derivatives and Baire 1 functions.
Countable tightness in the spaces of regular probability measures
We prove that if K is a compact space and the space P(K × K) of regular probability measures on K × K has countable tightness in its weak* topology, then L₁(μ) is separable for every μ ∈ P(K). It has been known that such a result is a consequence of Martin's axiom MA(ω₁). Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todorčević on measures on Rosenthal compacta.
Countably z-compact spaces
In this work we study countably z-compact spaces and z-Lindelof spaces. Several new properties of them are given. It is proved that every countably z-compact space is pseuodocompact (a space on which every real valued continuous function is bounded). Spaces which are countably z-compact but not countably compact are given. It is proved that a space is countably z-compact iff every countable z-closed set is compact. Characterizations of countably z-compact and z-Lindelof spaces by multifunctions...
Counting shape and homotopy types among fundamental absolute neighborhood retracts: an elementary approach.
Covariant and contravariant approaches to topology.
Cozero and Baire maps on products of uniform spaces
Cp-movable at infinity spaces, compact ANR divisors and property UVWn.
Criteria for Eberlein Compactness in Spaces of Continuous Functions.
Criteria of openness for relations
Criterion of Normality of the Completely Regular Topology of Separate Continuity
2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.For given completely regular topological spaces X and Y, there is a completely regular space X ~⊗ Y such that for any completely regular space Z a mapping f : X × Y ⊗ Z is separately continuous if and only if f : X ~⊗ Y→ Z is continuous. We prove a necessary condition of normality, a sufficient condition of collectionwise normality, and a criterion of normality of the products X ~⊗ Y in the case when at least one factor is scattered.
Curves which are continuous images of tree-like continua are movable
C(X) vs. C(X) modulo its socle
Let be the socle of C(X). It is shown that each prime ideal in is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential...