Domain-complete and LCS-complete Spaces

Domain-Representability of Certain Complete Spaces

In this paper we show that three major classes of topological spaces are domain-representable, i.e., homeomorphic to the space of maximal elements of some domain (=continuous dcpo) with the relative Scott topology. The three classes are: T3 subcompact spaces, strongly α-favorable spaces with a Gδ-diagonal or with a base of countable order, and complete quasi-developable T3-spaces. It follows th...

Complete Spaces

This paper is a continuation of [12]. First some definitions needed to formulate Cantor’s theorem on complete spaces and show several facts about them are introduced. Next section contains the proof of Cantor’s theorem and some properties of complete spaces resulting from this theorem. Moreover, countable compact spaces and proofs of auxiliary facts about them is defined. I also show the import...

Superstability of $m$-additive maps on complete non--Archimedean spaces

The stability problem of the functional equation was conjectured by Ulam and was solved by Hyers in the case of additive mapping. Baker et al. investigated the superstability of the functional equation from a vector space to real numbers. In this paper, we exhibit the superstability of $m$-additive maps on complete non--Archimedean spaces via a fixed point method raised by Diaz and Margolis.

Complete Generalized Metric Spaces

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

Complete Metric Spaces