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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
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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