$C$-separated sets in certain metric spaces

Separated finitely supported $Cb$-sets

The monoid $Cb$ of name substitutions and the notion of finitely supported $Cb$-sets introduced by Pitts as a generalization of nominal sets. A simple finitely supported $Cb$-set is a one point extension of a cyclic nominal set. The support map of a simple finitely supported $Cb$-set is an injective map. Also, for every two distinct elements of a simple finitely supported $Cb$-set, there exists...

Homeomorphisms of Compact Sets in Certain Hausdorff Spaces

In this paper, we construct a class of Hausdorff spaces with the property that nonempty compact subsets of these spaces that have the same cardinality are homeomorphic Theorem 3.7 . Conditions are given for these spaces to be compact Corollary 2.10 . Also, it is shown that these spaces contain compact subsets that are infinite Corollary 2.10 . This paper uses the Zermelo-Fraenkel axioms of set ...

Computational Models of Certain Hyperspaces of Quasi-metric Spaces

In this paper, for a given sequentially Yoneda-complete T1 quasi-metric space (X, d), the domain theoretic models of the hyperspace K0(X) of nonempty compact subsets of (X, d) are studied. To this end, the ω-Plotkin domain of the space of formal balls BX, denoted by CBX is considered. This domain is given as the chain completion of the set of all finite subsets of BX with respect to the Egli-Mi...

Concerning the Separability of Certain Locally Connected Metric Spaces

If a connected metric space S is locally separable, then S is separable. If a connected, locally connected, metric space S is locally peripherally separable, then S is separable. Furthermore if a connected, locally connected, complete metric space S satisfies certain "flatness" conditions, it is known to be separable. These "flatness" conditions are rather strong and involve both im kleinen and...

A Note on Naturally Ordered Sets in Semi-metric Spaces