Abstract
In this note Nagumo's definition of degree for compact perturbations of the identity in locally convex spaces is carried over to compact and approachable verturbations of the identity (c. f. Klee [1]) in arbitrary Hausdorff topological vector spaces, and it is shown, that the usual methods from Banach spaces can be used to prove a general form of Borsuk's theorem, open mapping theorems and some fixed point theorems.
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Kaballo, W. Zum Abbildungsgrad in Hausdorffschen Topologischen Vektorräumen. Manuscripta Math 8, 209–216 (1973). https://doi.org/10.1007/BF01297687
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DOI: https://doi.org/10.1007/BF01297687