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On open mappings, closed mappings, and ordinal invariants

Published online by Cambridge University Press:  17 April 2009

James R. Boone
James R. Boone
Affiliation:
Department of Mathematics, Texas A&M University, College Station Texas, USA.
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Abstract

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In this brief note new characterizations of open mappings and closed mappings are presented which involve the compact order of the domain. The paper answers some of the questions which resulted from the study of the ordinal monotonicity of pseudo-open mappings and thus constitutes an extension of that work. Another characterization of open mappings is introduced.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 19 , Issue 3 , December 1978 , pp. 325 - 328
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Arhangel'ski˘, A.V. and Franklin, S.P., “Ordinal invariants for topological spaces”, Michigan Math. J. 15 (1968), 313–320.Google Scholar
[2]Boone, James R., “Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants”, General Topology and Appl. 9 (1978), 243–251.CrossRefGoogle Scholar
[3]Boone, James R., Davis, Sheldon W. and Gruenhage, Gary, “Cardinal functions for fc-spaces”, Proc. Amev. Math. Soc. 68 (1978), 355–358.Google Scholar