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Sum Theorems for Countably Paracompact Spaces

Published online by Cambridge University Press:  20 November 2018

Henry Potoczny*
Affiliation:
University of Dayton, Dayton, Ohio
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In this paper, we extend the class of spaces to which the Σ and β theorems of Hodel apply, as well as the sum and subset theorems of [2]. Instead of the open cover definition of countable paracompactness, we utilize an equivalent formulation of countable paracompactness, due to Ishikawa [3].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Hodel, R. E., Total normality and the hereditary property, Proc. Amer. Math. Soc. 17 (1966), 462465.Google Scholar
2. Hodel, R. E., Sum theorems for topological spaces, Pacific J. Math. 30 (1969), 5965.Google Scholar
3. Ishikawa, T., On countably paracompact spaces, Proc. Japan Acad. 31 (1955), 686687.Google Scholar
4. Mack, J. E., Directed covers and paracompact spaces, Can. J. Math. 19 (1967), 649654.Google Scholar
5. Tamano, H., On paracompactness, Pacific J. Math. 10 (1960), 10431047.Google Scholar
6. Tamano, H., On compactifications, J. Math. Kyoto Univ. 1 (1962), 161193.Google Scholar
7. Zenor, P., A class of countably paracompact spaces, Proc. Amer. Math. Soc. 24 (1970), 258262.Google Scholar