Author(s):
Carter, Sheila 
; Carvalho, F. J. Craveiro de
Date: 2003
Persistent ID: http://hdl.handle.net/10316/11441
Origin: Estudo Geral - Universidade de Coimbra
Document details
Locally Sierpinski quotients
Description
Given any non-trivial, connected topological space X, it is possible to de ne an equivalence relation ~ on it such that the topological quotient space X/ ~ 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 di erent Centro de Matemática da Universidade de Coimbra
Given any non-trivial, connected topological space X, it is possible to de ne an equivalence relation ~ on it such that the topological quotient space X/ ~ 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 di erent Centro de Matemática da Universidade de Coimbra
Document Type
Preprint
Language English
Language English
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