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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Dimension of stratifiable spaces


Author: Shinpei Oka
Journal: Trans. Amer. Math. Soc. 275 (1983), 231-243
MSC: Primary 54E20; Secondary 54E18, 54F45
MathSciNet review: 678346
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Abstract: We define a subclass, denoted by $ E{M_3}$, of the class of stratifiable spaces, and obtain several dimension theoretical results for $ E{M_3}$ including the coincidence theorem for dim and Ind. The class $ E{M_3}$ is countably productive, hereditary, preserved under closed maps and, furthermore, the largest subclass of stratifiable spaces in which a harmonious dimension theory can be established.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0678346-6
Keywords: Stratifiable space, $ \sigma $-space, $ E$-net, $ LE$-net, $ E$-quartet, $ E$-map, fiber product
Article copyright: © Copyright 1983 American Mathematical Society