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On the Dimension of Paracompact Hausdorff Spaces

Published online by Cambridge University Press:  22 January 2016

Keiô Nagami
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This short note gives the generalized sum theorem for Lebesgue dimension of paracompact Hausdorff spaces. Our theorem, though it is a generalization of Mr. Morita’s sum theorem for fully normal spaces [3, Theorem 3. 2] which is essentially based on his generalized sum theorem for normal spaces [3, Theorem 3.1], is obtained by very brief arguments, using only the usual sum theorem for normal spaces.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 8 , February 1955 , pp. 69 - 70
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1955

References

[1] Hemmingsen, E.: Some theorems in dimension theory for normal Hausdorff spaces, Duke Math. J. 13 (1946) 495–504.Google Scholar
[2] Morita, K.: Star-finite coverings and the star-finite property, Mathematica Japonicae 1 (1948) 60–68.Google Scholar
[3] Morita, K.: On the dimension of normal spaces II, J. Math. Soc. Japan 20 (1950) 16–33.Google Scholar
[4] Nagami, K.: Paracompactness and strong screenability, Nagoya Math. J. 8 (1955) 79–102.Google Scholar