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arXiv · 1103.3710

Some steps on short bridges: Non-metrizable surfaces and CW-complexes

Mathieu Baillif
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Abstract

Among the classical variants of the Prüfer surface, some are homotopy equivalent to a CW-complex (namely, a point or a wedge of a continuum of circles) and some are not. The obstruction comes from the existence of uncountably many `infinitesimal bridges' linking two metrizable open subsurfaces inside the surface. We show that any non-metrizable surface that possesses such a system of infinitesimal bridges cannot be homotopy equivalent to a CW-complex. More than for the result on its own, we were motivated by trying to blend elementary techniques of algebraic and set-theoretic topology.

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Mathieu Baillif. 2011-09-16. Some steps on short bridges: Non-metrizable surfaces and CW-complexes. https://arxiv.org/abs/1103.3710

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