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Every Countable Regular Space Without Isolated Points is Connectifiable

Published online by Cambridge University Press:  20 November 2018

V. Tzannes*
Affiliation:
Department of Mathematics, University of Patras Patras Greece
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Abstract

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It is proved that every countable regular space without isolated points can be embedded densely in a connected Hausdorff space with a dispersion point.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Levy, R., Countable spaces without points of first countability, Pacific J. Math. (2) 70(1977), 391399.Google Scholar
2. Ori, R. G. and Rajagopalan, M., On countable connected locally connected almost regular Urysohn spaces, Topology Appl. 17(1984), 157171.Google Scholar
3. Roy, P., A countable connected Urysohn space with a dispersion point, Duke Math. J. 33(1966), 331333.Google Scholar
4. Sierpinski, W., Sur une propriété topologique des ensembles denombrables denses en soi, Fund. Math. 1(1920), 1116.Google Scholar
5. Watson, S., Embedding a Space in a Connected Space, York University, Report No. 91–03.Google Scholar