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On the connectification of a space by a countable point set

Published online by Cambridge University Press:  09 April 2009

Gary Miller  and
B. J. Pearson
Gary Miller
Affiliation:
University of Missouri at Kansas City
B. J. Pearson
Affiliation:
University of Missouri at Kansas City
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In this note we define a rather pathological connectedness property of Hausdorff spaces which is stronger than ordinary connectedness. We obtain a few basic properties of such spaces and derive a method for constructing them. It turns out that countable Hausdorff spaces having the connectedness property are as easily constructed as uncountable ones. Hence we have still another method for constructing countable connected Hausdorff spaces.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 67 - 70
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Bing, R. H., ‘A countable connected Hausdorff space’, Proc. Amer. Math. Soc. 59 (1953), 474.Google Scholar
[2]Brown, M., ‘A countable connected Hausdorff space’, Bull. Amer. Math. Soc. 59 (1953), 367.Google Scholar
[3]Hewitt, E., ‘On two problems of Urysohn’, Annals of Mathematics, 47 (1946), 503–509.Google Scholar
[4]Martin, J., ‘A countable connected Hausdorff space with a dispersion point’, Duke Math. J. 33 (1966), 165–167.Google Scholar
[5]Urysohn, P., ‘Über die Mächtigkeit der Zusammenhängen Mengen’, Mathematische Annalen, 94 (1925), 262–295.Google Scholar