Categories of Wallman extendible functions
Čech-Stone-like compactifications for general topological spaces
The problem whether every topological space has a compactification such that every continuous mapping from into a compact space has a continuous extension from into is answered in the negative. For some spaces such compactifications exist.
Classical-type characterizations of non-metrizable ANE(n)-spaces
The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is (resp., ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.
Collectionwise normality and extensions of continuous functions
Collectionwise normality and the extension of functions on product spaces
Compactifications and -separation
Compactifications with finite remainders
Compactness of trajectories of dynamical systems in complete uniform spaces
Completion as reflection
Continuous extensions: answer to a question of Hanner
Continuous extensions of multifunctions
Continuous functions between Isbell-Mrówka spaces
Let be the Isbell-Mr’owka space associated to the -family . We show that if is a countable subgroup of the group of all permutations of , then there is a -family such that every can be extended to an autohomeomorphism of . For a -family , we set for all . It is shown that for every there is a -family such that . As a consequence of this result we have that there is a -family such that whenever and , where for . We also notice that there is no -family such...
Continuous selections and approximations in α-convex metric spaces
In the paper, the notion of a generalized convexity was defined and studied from the view-point of the selection and approximation theory of set-valued maps. We study the simultaneous existence of continuous relative selections and graph-approximations of lower semicontinuous and upper semicontinuous set-valued maps with α-convex values having nonempty intersection.
Correction to the paper: On linear functorial operators extending pseudometrics
Correction to the paper: Random coincidence degree theory with applications to random differential inclusions
Covariant and contravariant approaches to topology.
Does C* -embedding imply C*-embedding in the realm of products with a non-discrete metric factor?
The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.
Dugundji extenders and retracts on generalized ordered spaces
For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an -extender (resp. -extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X; (iii) there is a continuous -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology and...
Dugundji spaces and topological groups
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