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The boundedness principle characterizes second category subsets

Published online by Cambridge University Press:  17 April 2009

Kevin A. Broughan
Kevin A. Broughan
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand.
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Abstract

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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
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 257 - 265
Copyright
Copyright © Australian Mathematical Society 1977

References

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