An Embedding of Space of Continuous Functions of a Hausdorff, Locally Compact Space

Abstract

Assume X is a Hausdorff, locally compact space. This paper demonstrates the space of continuous functions on K(X), which is, the open sets in the topology of Vietoris on the collection of all compact subspaces of X embedded into K(C(K(X)) with Fell topology. Combining with another embedding theorem, it is confirmed that C(X) is placed within K(C(K(X)))