Countable KC Functions and Inversely Countable KC Functions

Abstract

In this paper, we introduce a new class of functions to be called countable KC and inversely countable KC functions. We study some relations between countable KC functions and inversely countable KC functions. We prove that if f is a continuous function from a space X to a Frechet, countable KC space Y, then $f(H)$ is closed in Y whenever H is a limit point compact set of X. It is also proved that if f is a countable KC function from a Frechet space X to a compact space Y, having closed point inverses, then f is continuous.