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ON DENSE EMBEDDINGS INTO MOORE SPACES WITH THE BAIRE PROPERTY

  • DAVID L. FEARNLEY (a1) and LAWRENCE FEARNLEY (a2)

Abstract

We demonstrate a construction that will densely embed a Moore space into a Moore space with the Baire property when this is possible. We also show how this technique generates a new ‘if and only if’ condition for determining when Moore spaces can be densely embedded in Moore spaces with the Baire property, and briefly discuss how this condition can can be used to generate new proofs that certain Moore spaces cannot be densely embedded in Moore spaces with the Baire property.

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Copyright

Corresponding author

For correspondence; e-mail: axiom10@gmail.com

References

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[1]Bing, R. H., ‘Metrization of topological spaces’, Canad. J. Math. 3 (1951), 175186.
[2]Fearnley, D. L., ‘A Moore space with a σ-discrete π-base which cannot be densely embedded in any Moore space with the Baire property’, Proc. Amer. Math. Soc. 127(10) (1999), 30953100.
[3]Fitzpatrick, B., ‘On dense subspaces of Moore spaces, II’, Fund. Math. 61 (1967), 9192.
[4]Moore, R. L., Foundations of Point Set Theory, American Mathematical Society Colloquium Publications, 13 (American Mathematical Society, Providence, RI, 1962), revised edition.
[5]Reed, G. M., On Completeness Conditions in Moore Spaces, Lecture Notes in Mathematics, 378 (Springer, New York, 1974), pp. 368384.
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ON DENSE EMBEDDINGS INTO MOORE SPACES WITH THE BAIRE PROPERTY

  • DAVID L. FEARNLEY (a1) and LAWRENCE FEARNLEY (a2)

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