Geometric Tools

David Gauld ()
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David Gauld: University of Auckland, Department of Mathematics

Chapter Chapter 3 in Non-metrisable Manifolds, 2014, pp 37-48 from Springer

Abstract: Abstract This chapter gathers together some useful geometric tools for later reference. The first section presents Morton Brown’s theorem which tells us that if a space is the monotone union of a countable sequence of open subsets each homeomorphic to $${\mathbb R}^n$$ R n then the space itself is homeomorphic to $${\mathbb R}^n$$ R n . We then discuss Brown’s Collaring Theorem, which enables us to impose a product structure on a neighbourhood of a metrisable component of the boundary of a manifold. Finally we consider handlebodies, which provide a useful decomposition of a metrisable manifold into simple pieces.

Keywords: Half Plane; Simplicial Complex; Boundary Component; Cell Complex; Algebraic Topology (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-287-257-9_3

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DOI: 10.1007/978-981-287-257-9_3

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