A research on characterizations of semi- spaces.
In this paper, the α waybelow relation, which is determined by O2-convergence, is characterized by the order on a poset, and a sufficient and necessary condition for O2-convergence to be topological is obtained.
We study best approximation in -normed spaces via a general common fixed point principle. Our results unify and extend some known results of Carbone [ca:pt], Dotson [do:bs], Jungck and Sessa [ju:at], Singh [si:at] and many of others.
A retractible non-locally connected dendroid is constructed.
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 ...
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 rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. The first complete rigid space was published in 1981 in [2]. Clearly a rigid space is a trivial-dual space, and admits no compact endomorphisms. In this paper a modification of the original construction results in a rigid space which is, however, the domain space of a compact operator, answering a question that was first raised soon after the existence of complete rigid spaces was...
In this paper we develop the semifilter approach to the classical Menger and Hurewicz properties and show that the small cardinal is a lower bound of the additivity number of the -ideal generated by Menger subspaces of the Baire space, and under every subset of the real line with the property is Hurewicz, and thus it is consistent with ZFC that the property is preserved by unions of less than subsets of the real line.