Topological Spaces

Daniel Alpay
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Daniel Alpay: Ben-Gurion University of the Negev

Chapter Chapter 3 in An Advanced Complex Analysis Problem Book, 2015, pp 121-198 from Springer

Abstract: Abstract Topological and metric spaces permeate complex analysis in numerous places. For instance, the space $$\mathcal{H}(\Omega) $$ of functions analytic in some open domain $$\Omega $$ is a Frechet space (and moreover, a Montel space). Hilbert and Banach spaces of analytic functions also play an important role. These examples are in fact instances of topological vector spaces. As another example, Riemann surfaces are in particular analytic manifolds, and as such are special cases of topological spaces, and in fact of metric spaces.

Keywords: Open Subset; Riemann Surface; Topological Space; Compact Space; Open Ball (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-16059-7_3

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