Tietze Extension Theorem for n-dimensional Spaces
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 f...
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| Format: | Article |
| Language: | English |
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Sciendo
2014-03-01
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| Series: | Formalized Mathematics |
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| Online Access: | https://doi.org/10.2478/forma-2014-0002 |
| Summary: | 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 with a convex compact subset of En with a non-empty interior. This article is based on [20]; [23] and [22] can also serve as reference books. |
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| ISSN: | 1898-9934 |