Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 46, No. 2, pp. 357361 (2005) 

Locally Sierpinski QuotientsSheila Carter and F. J. Craveiro de CarvalhoSchool of Mathematics, University of Leeds, Leeds LS2 9JT, U. K. email: S.Carter@leeds.ac.uk; Departamento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal email: fjcc@mat.uc.ptAbstract: Given any nontrivial, connected topological space $X$, it is possible to define an equivalence relation $\sim$ on it such that the topological quotient space $X/\sim$ is the Sierpinski space. Locally Sierpinski spaces are generalizations of the Sierpinski space and here we address the following question. Does a statement like the one above hold if ``Sierpinski'' is replaced by (proper) ``locally Sierpinski''? The answer is no and we will give below a few counterexamples. The situation where a homeomorphism group acts on a topological $n$manifold will also be analysed, the conclusion being that the cases $n=1, n>1$ are radically different. Classification (MSC2000): 54F65 Full text of the article:
Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.
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