Locally Sierpinski quotients
Locally Sierpinski quotients
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
- University of Coimbra Portugal
Topological characterizations of particular spaces, Sierpinski space, satellite, quotient, Quotient spaces, decompositions in general topology, group action, Transformation groups and semigroups (topological aspects)
Topological characterizations of particular spaces, Sierpinski space, satellite, quotient, Quotient spaces, decompositions in general topology, group action, Transformation groups and semigroups (topological aspects)
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