Two countable Hausdorff almost regular spaces every contiunous map of which into every Urysohn space is constant

V. Tzannes

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-6

Abstract:

We construct two countable, Hausdorff, almost regular spaces I ( S ) , I ( T ) having the following properties: (1) Every continuous map of I ( S ) (resp, I ( T ) ) into every Urysohn space is constant (hence, both spaces are connected). (2) For every point of I ( S ) (resp. of I ( T ) ) and for every open neighbourhood U of this point there exists an open neighbourhood V of it such that V ⫅ U and every continuous map of V into every Urysohn space is constant (hence both spaces are locally connected). (3) The space I ( S ) is first countable and the space I ( T ) nowhere first countable. A consequence of the above is the construction of two countable, (connected) Hausdorff, almost regular spaces with a dispersion point and similar properties. Unfortunately, none of these spaces is Urysohn.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:425219

DOI: 10.1155/S0161171291000959

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