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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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.

References [Enhancements On Off] (What's this?)

  • [A$ _{1}$] C. E. Aull, Quasi-developments and $ \delta \theta $-bases, J. London Math. Soc. (2) 9 (1974), 197-204. MR 0388334 (52:9171)
  • [A$ _{2}$] -, Some properties involving base axioms and metrizability, Lecture Notes in Math., vol. 378, Springer-Verlag, Berlin and New York, 1974, pp. 41-45. MR 0415575 (54:3660)
  • [BB] H. R. Bennett and E. S. Berney, Spaces with $ \sigma $-minimal bases, Topology Proceedings 2 (1977), 1-10. MR 540595 (80k:54050)
  • [BL] H. R. Bennett and D. J. Lutzer, Ordered spaces with $ \sigma $-minimal bases, Topology Proceedings 2 (1977), 371-382. MR 540616 (80j:54027)

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Keywords: $ \sigma $-minimal base, weight, product space, perfect map
Article copyright: © Copyright 1981 American Mathematical Society

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