We study the behavior of certain spaces and their compactificability classes at infinity. Among other results we show that every noncompact, locally compact, second countable Hausdorff space X such that each neighborhood of infinity (in the Alexandroff compactification) is uncountable, has (X) = (R). We also prove some criteria for (non-) comparability of the studied classes of mutual compactif...

For the usual norm on spaces C(K) and C b (Ω) of all continuous functions on a compact Hausdorff space K (all bounded continuous functions on a locally compact Hausdorff space Ω), the following equalities are proved: lim t→0+ ||f + tg|| C(K) − ||f || C(K) t = max x∈{z | |f (z)|=||f ||} Re(e −i arg f (x) g(x)). and lim t→0+ ||f + tg|| C b (Ω) − ||f || C b (Ω) t = inf δ>0 sup x∈{z | |f (z)|≥||f |...

This paper is centered on an extremely general problem: Problem. Is it consistent (perhaps modulo large cardinals) that a locally compact space X must be the union of countably many ω-bounded subspaces if every closed discrete subspace of X is countable [in other words, if X is ω1-compact]? A space is ω-bounded if every countable subset has compact closure. This is a strengthening of countable ...

we investigate compact composition operators on ceratin lipschitzspaces of analytic functions on the closed unit disc of the plane.our approach also leads to some results about compositionoperators on zygmund type spaces.

We study locally compact, geodesically complete, CAT $$(\kappa )$$ spaces ( $$\hbox {GCBA}^\kappa $$ -spaces). prove a Croke-type local volume estimate only depending on the dimension of these spaces. show that doubling condition, with respect to natural measure, implies pure-dimensionality. Then we consider -spaces satisfying uniform packing condition at some fixed scale $$r_0$$ or arbitrarily...

Compact fuzzy topological spaces were first introduced by Chang [3]. o-compact fuzzy topological spaces were introduced by Gantner et al. [4]. Abd El-Monsef et al. [1] introduced the notion of e-aimost compact fuzzy topological spaces. Mashhour et al. [8] introduced the notion of bifuzzy topological spaces and defined the notion of o-compactness in those spaces. In this paper, we obtain some ne...

This paper represents a continuation of our programme [16, 13] of extending various concepts of general topology from the setting of Hausdorff (or, at most, 7̂ ) spaces, in which they are usually embedded, to the larger classes of spaces we need to consider in the theory of computation. The topic of compactification poses an obvious challenge to this programme, since only a Tychonoff space can h...

In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

In this paper, by using C-sequentially sign property for bifunctions, we provide sufficient conditions that ensure the existence of solutions of some vector equilibrium problems in Hausdorff topological vector spaces which ordered by a cone. The conditions which we consider are not imposed on the whole domain of the operators involved, but just on a locally segment-dense subset of the domain.