文章基本信息

标题：Concerning Cut Point Spaces of Order Three
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作者：D. Daniel ; William S. Mahavier
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2007
卷号：2007
DOI：10.1155/2007/10679
出版社：Hindawi Publishing Corporation
摘要：A point p of a topological space X is a cut point of X if X−{p} is disconnected. Further, if X−{p} has precisely m components for some natural number m≥2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y, we will say that Y is a cut point space. Herein we construct a space S so that S is a connected Hausdorff space and each point of S is a cut point of order three. We also note that there is no uncountable separable cut point space with each point a cut point of order three and therefore no such space may be embedded in a Euclidean space.