On two problems of Harris concerning RC-proximities

Sharma, P. L.; Naimpally, S. A.

doi:10.1090/S0002-9939-1972-0292022-1

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

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On two problems of Harris concerning RC-proximities
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by P. L. Sharma and S. A. Naimpally PDF

Proc. Amer. Math. Soc. 32 (1972), 312 Request permission

Abstract:

We give an example that settles the first and third problems posed recently by Douglas Harris [1]. The example shows that comparable RC-proximities on an RC-regular space need not give rise to comparable regular-closed embeddings, and that an RC-regular space need not have a largest regular-closed embedding.

References

Douglas Harris, Regular-closed spaces and proximities, Pacific J. Math. 34 (1970), 675–685. MR 284974
Manuel P. Berri and R. H. Sorgenfrey, Minimal regular spaces, Proc. Amer. Math. Soc. 14 (1963), 454–458. MR 152978, DOI 10.1090/S0002-9939-1963-0152978-9