The Locally K-Convex Spaces Cn (X), C ∞(X)

The Cⁿ -functions have been systematically studied by W. Schikhof [4]. The locally K-convex space Cⁿ(X) has been studied principally by N. De Grande-De Kimpe [1]. In this paper we present results characterizing the compactoids in Cⁿ(X), in the spirit of Martínez-Maurica and Navarro [3].

We also study the structure of Cⁿ(X) presenting conditions for its normability and metrizability.