Embedding planar compacta in planar continua with application: homotopic maps between planar Peano continua are characterized by the fundamental group homomorphism

Paul Fabel

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arXiv · 0902.1723

Embedding planar compacta in planar continua with application: homotopic maps between planar Peano continua are characterized by the fundamental group homomorphism

Paul Fabel

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Abstract

A planar compactum with connected complement can be an embedded in a cellular continuum by attaching a null sequence of arcs. Two based maps f and g from a planar Peano continuum X to a planar set Y are homotopic iff f and g induce the same homomorphism between fundamental groups.

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Paul Fabel. 2009-03-22. Embedding planar compacta in planar continua with application: homotopic maps between planar Peano continua are characterized by the fundamental group homomorphism. https://arxiv.org/abs/0902.1723

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