Loading...
Thumbnail Image
Item

The boundedness principle characterizes second category subsets

Abstract
Converses are proved for the Osgood (the Principle of Uniform Boundedness), Dini, and other well known. theorems. The notion of a continuous step function on a topological space is defined and a class of spaces identified for which each lower semicontinuous function is the pointwise limit of a monotonically increasing sequence of step functions.
Type
Journal Article
Type of thesis
Series
Citation
Broughan, K. A. (1977). The boundedness principle characterizes second category subsets. Bulletin of the Australian Mathematical Society, 16(2), 257–265. http://doi.org/10.1017/S0004972700023285
Date
1977
Publisher
Degree
Supervisors
Rights
This article is published in the Bulletin of the Australian Mathematical Society. © 1977, Australian Mathematical Society. Used with permission