Displaying similar documents to “Brouwer Invariance of Domain Theorem”

Tietze Extension Theorem for n-dimensional Spaces

Karol Pąk (2014)

Formalized Mathematics

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In this article we prove the Tietze extension theorem for an arbitrary convex compact subset of εn with a non-empty interior. This theorem states that, if T is a normal topological space, X is a closed subset of T, and A is a convex compact subset of εn with a non-empty interior, then a continuous function f : X → A can be extended to a continuous function g : T → εn. Additionally we show that a subset A is replaceable by an arbitrary subset of a topological space that is homeomorphic...

On a characterization of the unit interval in terms of clones

Artur Barkhudaryan (1999)

Commentationes Mathematicae Universitatis Carolinae

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This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.

Carathéodory balls and norm balls in H p , n = z n : z p < 1

Binyamin Schwarz, Uri Srebro (1996)

Banach Center Publications

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It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on H p , n = z n : z p < 1 which are balls with respect to the complex l p norm in n are those centered at the origin.