A Remark on the Topological Entropy of Homeomorphisms.
A remark on the uniformization in metric ѕpaces
A remark on the uniqueness of quasi continuous functions.
A remark on the weak topology of the Hilbert space
A retractible non-locally connected dendroid
A retractible non-locally connected dendroid is constructed.
A reverse viewpoint on the upper semicontinuity of multivalued maps
For a multivalued map between topological spaces, the upper semifinite topology on the power set is such that is upper semicontinuous if and only if it is continuous when viewed as a singlevalued map . In this paper, we seek a result like this from a reverse viewpoint, namely, given a set and a topology on , we consider a natural topology on , constructed from satisfying if , and we give necessary and sufficient conditions to the upper semicontinuity of a multivalued map ...
A revised closed graph theorem for quasi-Suslin spaces
Some results about the continuity of special linear maps between -spaces recently obtained by Drewnowski have motivated us to revise a closed graph theorem for quasi-Suslin spaces due to Valdivia. We extend Valdivia’s theorem by showing that a linear map with closed graph from a Baire tvs into a tvs admitting a relatively countably compact resolution is continuous. This also applies to extend a result of De Wilde and Sunyach. A topological space is said to have a (relatively countably) compact...
A sandwich with convexity for set-valued functions.
A selection theorem
A selection theorem for Boolean correspondences.
A selection theorem for open-graph multifunctions
A selection theory for multiple-valued functions in the sense of Almgren.
A simplicial monotone-light factorization theorem
A simultaneous selection theorem
We prove a theorem that generalizes in a way both Michael's Selection Theorem and Dugundji's Simultaneous Extension Theorem. We use it to prove that if K is an uncountable compact metric space and X a Banach space, then C(K,X) is isomorphic to C(𝓒,X) where 𝓒 denotes the Cantor set. For X = ℝ, this gives the well known Milyutin Theorem.
A spectral characterization of skeletal maps
We prove that a map between two realcompact spaces is skeletal if and only if it is homeomorphic to the limit map of a skeletal morphism between ω-spectra with surjective limit projections.
A strengthening of the Katětov-Tong insertion theorem
Normal spaces are characterized in terms of an insertion type theorem, which implies the Katětov-Tong theorem. The proof actually provides a simple necessary and sufficient condition for the insertion of an ordered pair of lower and upper semicontinuous functions between two comparable real-valued functions. As a consequence of the latter, we obtain a characterization of completely normal spaces by real-valued functions.
A study of -spaces and -spaces.
A study on some new types of Hardy-Hilbert's integral inequality.
A subclass of the class MOBI
A subspace of and its connexions with the maximal ring of quotients