Vector-valued continuous functions with compact-Gδ-open topology

In this paper, we study compact-[Formula: see text]-open topology [Formula: see text] on the set [Formula: see text] of all continuous functions from a completely regular space [Formula: see text] to a locally convex space [Formula: see text]. We investigate the local convexity of the space [Formula: see text] equipped with [Formula: see text]-topology and compare the pointwise topology, compact open topology and [Formula: see text]-topology on [Formula: see text]. Metrizability, submetrizability and separability are also studied.