Construction of spaces with a 𝜎-minimal base

Burke, Dennis K.

doi:10.1090/S0002-9939-1981-0593483-6

Construction of spaces with a $\sigma$-minimal base
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Proc. Amer. Math. Soc. 81 (1981), 329-332 Request permission

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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