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The regularity series of a convergence space

Published online by Cambridge University Press:  17 April 2009

G.D. Richardson  and
D.C. Kent
G.D. Richardson
Affiliation:
Department of Mathematics, East Carolina University, Greenville, North Carolina, USA;
D.C. Kent
Affiliation:
Department of Pure and Applied Mathematics, Washington State University, Pullman, Washington, USA.
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Abstract

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The regularity series, or briefly R-series, of a convergence space is an ordinal sequence of spaces leading to the regular modification of the space. The behavior of this series is studied relative to such basic constructs as products, subspaces, and various quotient maps. Upper bounds on the length of the R-series are obtained for several classes of spaces. This series can be employed to construct regular completions and compactifications.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 1 , August 1975 , pp. 21 - 44
Copyright
Copyright © Australian Mathematical Society 1975

References

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