Compact subsets of a Tychonoff set

Uniform Convergence to a Left Invariance on Weakly Compact Subsets

Let  $left{a_alpharight}_{alphain I}$ be a bounded net in a Banach algebra $A$ and $varphi$ a nonzero multiplicative linear functional on $A$. In this paper, we deal with the problem of when $|aa_alpha-varphi(a)a_alpha|to0$ uniformly for all $a$ in weakly compact subsets of $A$. We show that Banach algebras associated to locally compact groups such  as Segal algebras and $L^1$-algebras are resp...

Certain Weakly Generated Noncompact, Pseudo-compact Topologies on Tychonoff Cubes

Given an uncountable cardinal א, the product space I, I = [0, 1], is called a Tychonoff cube. A collection of closed subsets of a subspace Y of a Tychonoff cube I that covers Y determines a weak topology for Y . The collection of compact subsets of I that have a countable dense subset covers I. It is known from work of the author and I. Ivanšić that the weak topology generated by this collectio...

Near PS-compact L-subsets

In this paper, the new concept of near PS-compactness in L-topological spaces is introduced. It is defined for any L-subset. Its characterizations and topological properties are systematically studied. And the relationship is exposed between near PScompactness and PS-compactness, and also fuzzy compactness. 2003 Elsevier Inc. All rights reserved.

Extremal problems among subsets of a set

This paper is a survey of open problems and results involving extremal size of collections of subsets of a finite set subject to various restrictions, typically on intersections of members .

Domain representations of spaces of compact subsets