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 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.