A new compactness type topological property

Abstract

By a gauge on a topological space we shall mean a mapping that assigns each element in the space an open neighbourhood. We investigate some topological properties which can be characterized using gauges. The main property we will consider is the gauge compactness. Some problems and possible future work are listed at the end of the paper.
Keywords: Gauge; M-uniformly continuous mapping; gauge compact space

Quaestiones Mathematicae 28(2005), 459–469