Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 2, pp. 357-361 (2005)
Locally Sierpinski Quotients
Sheila Carter and F. J. Craveiro de CarvalhoSchool of Mathematics, University of Leeds, Leeds LS2 9JT, U. K. e-mail: S.Carter@leeds.ac.uk; Departamento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal e-mail: email@example.com
Abstract: Given any non-trivial, 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
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Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.