Weakly closed multifunctions and paracompactness.
Weakly confluent mappings and a classification of continua
Weakly continuous functions of Baire class 1.
For a compact Hausdorff space K and a Banach space X, let WC(K,X) denote the space of X-valued functions defined on K, that are continuous when X has the weak topology. In this note by a simple Banach space theoretic argument, we show that given f belonging to WC(K,X) there exists a net {fa} contained in C(K,X) (space of norm continuous functions) such that fa --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.
Weakly fuzzy topological entropy
In 2005, İ. Tok fuzzified the notion of the topological entropy R. A. Adler et al. (1965) using the notion of fuzzy compactness of C. L. Chang (1968). In the present paper, we have proposed a new definition of the fuzzy topological entropy of fuzzy continuous mapping, namely weakly fuzzy topological entropy based on the notion of weak fuzzy compactness due to R. Lowen (1976) along with its several properties. We have shown that the topological entropy R. A. Adler et al. (1965) of continuous mapping...
Weakly -continuous functions.
Weight and metrizability of inverses under hereditarily irreducible mappings.
Well posedness for evolution inclusions.
When a composition algebra is barrelled?
When is domain representable
Let M be a metrizable group. Let G be a dense subgroup of . We prove that if G is domain representable, then . The following corollaries answer open questions. If X is completely regular and is domain representable, then X is discrete. If X is zero-dimensional, T₂, and is subcompact, then X is discrete.
When finely continuous functions are of the first class of Baire
Which topological spaces have a weak reflection in compact spaces?
The problem, whether every topological space has a weak compact reflection, was answered by M. Hušek in the negative. Assuming normality, M. Hušek fully characterized the spaces having a weak reflection in compact spaces as the spaces with the finite Wallman remainder. In this paper we prove that the assumption of normality may be omitted. On the other hand, we show that some covering properties kill the weak reflectivity of a noncompact topological space in compact spaces.
Whitney continua of graphs admit all homotopy types of compact connected ANRs
Whitney maps-a non-metric case
It is shown that there is no Whitney map on the hyperspace for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).