Measure theoretic techniques in topology and mappings of replete and measure replete spaces

Abstract

We prove in this paper several results on lattice related measures and. images of such measures under mappings. If we apply these to various areas of point set topology we obtain as corollaries many known and new results on sequential compactness, repleteness,and measure repleteness -areas of recent considerable interest to mathematicians.

On Subspaces of Replete and Measure Replete Spaces

“…Introduction. Measure replete spaces have been investigated in special topological settings by Varadarajan [14], Moran [11], Gardner [7], and others, and in the abstract lattice setting by Bachman and Sultan [4], and Szeto [13]. In this paper, we let L be a lattice of subsets of the set X such that L is measure replete and we investigate measure repleteness with respect to various lattices of subsets of a subset E of X.…”

On regular extensions of measures

“…O Introduction* In previous papers see [1][2][3][4]18, 19] we were concerned with regular extensions of measures and their applications to several different areas of mathematics. Typically one was given a μeMRi^i) and conditions were given for when μ extended to a veMR(Jέf 2 ) where J^ci^ were sublattices of 2 Σ .…”