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Construction of spaces with a $ \sigma $-minimal base


Author: Dennis K. Burke
Journal: Proc. Amer. Math. Soc. 81 (1981), 329-332
MSC: Primary 54G99; Secondary 54A25
MathSciNet review: 593483
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Abstract: Using product spaces, a method is given for constructing and recognizing certain spaces with a $ \sigma $-minimal base. This technique shows that every topological space can be embedded as a closed subspace of a space with a $ \sigma $-minimal base; hence a $ \sigma $-minimal base, by itself, does not imply any nontrivial closed hereditary topological property. It is also shown that any space $ Y$ can be expressed as the open perfect image of some space with a $ \sigma $-minimal base. Examples are given, illustrating a surprisingly large class of product spaces with a $ \sigma $-minimal base.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593483-6
Keywords: $ \sigma $-minimal base, weight, product space, perfect map
Article copyright: © Copyright 1981 American Mathematical Society