Continuity of multifunctions with respect to local sieves and quasi-uniform convergence
Continuity of Nemyckij's operator in Hölder spaces
Continuity of semigroup actions.
Continuity of the Hausdorff dimension for invariant subsets of interval maps.
Continuity of the superposition of set-valued functions.
Continuity points in
Continuity properties of convex-type set-valued maps.
Continuity properties up to a countable partition.
Approximation and rigidity properties in renorming constructions are characterized with some classes of simple maps. Those maps describe continuity properties up to a countable partition. The construction of such kind of maps can be done with ideas from the First Lebesgue Theorem. We present new results on the relationship between Kadec and locally uniformly rotund renormability as well as characterizations of the last one with the simple maps used here.
Continuous actions of pseudocompact groups and axioms of topological group
In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces that gives some new examples and statements for the -theory and theory of topologically homogeneous spaces.
Continuous depencence of on as a selection property.
Continuous extenders for pseudometrics
Continuous extenders in normal and collectionwise normal spaces
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 functions on countable subspaces
Continuous functions on products of topological spaces
Continuous images and other topological properties of Valdivia compacta
We study topological properties of Valdivia compact spaces. We prove in particular that a compact Hausdorff space K is Corson provided each continuous image of K is a Valdivia compactum. This answers a question of M. Valdivia (1997). We also prove that the class of Valdivia compacta is stable with respect to arbitrary products and we give a generalization of the fact that Corson compacta are angelic.
Continuous images of ordered compacta and hereditarily locally connected continua
Continuous mappings and Cauchy sequences