Finitely chainable and totally bounded metric spaces: Equivalent characterizations

Totally Bounded Metric Spaces

The papers [19], [9], [1], [4], [20], [2], [18], [13], [5], [8], [14], [21], [7], [15], [12], [11], [17], [6], [10], [16], and [3] provide the terminology and notation for this paper. For simplicity we follow the rules: M is a metric space, c, g are elements of the carrier of M , F is a family of subsets of the carrier of M , A, B are subsets of the carrier of M , f is a function, n, m, p, k ar...

FUZZY BOUNDED SETS AND TOTALLY FUZZY BOUNDED SETS IN I-TOPOLOGICAL VECTOR SPACES

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

Chainable and Circularly Chainable Co-r.e. Sets in Computable Metric Spaces

We investigate under what conditions a co-recursively enumerable set S in a computable metric space (X, d, α) is recursive. The topological properties of S play an important role in view of this task. We first study some properties of computable metric spaces such as the effective covering property. Then we examine co-r.e. sets with disconnected complement, and finally we focus on study of chai...

Characterizations of Compactness for Metric Spaces

Characterizations of Sobolev Inequalities on Metric Spaces

We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.