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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

[1]Broughan, K.A., “Metrization of spaces having Čech dimension zero”, Bull. Austral. Math. Soc. 9 (1973), 161–168.CrossRefGoogle Scholar
[2]Engelking, R., Outline of general topology (translated by Sieklucki, K.. North-Holland, Amsterdam; PWN-Polish Scientific Publishers, Warsaw; 1968).Google Scholar
[3]Royden, H.L., Real analysis, second edition (Macmillan, New York; Collier-Macmillan, London; 1968).Google Scholar
[4]Thornton, Melvin C., “Characterizing topologies by functions”, Proc. Amer. Math. Soc. 36 (1972), 613–614.CrossRefGoogle Scholar