Comparison of topologies on function spaces

Topologies between compact and uniform convergence on function spaces

“…Since (6) implies (3), it remains only to show that (7) implies (4) and (5). Suppose that X contains a dense a-compact subset D. Let I be any element of Ca(X).…”

“…This paper studies two topologies on [6] to be the proper setting to study sequences of functions which converge uniformly on compact subsets. One of the distinguishing features of this topology is that whenever x is locally compact the compact-open topology on C(X) is the coarsest topology making the evaluation map e:X C(X)--.…”

Completeness properties of the pseudocompact-open topology on C(X)

“…A r e n s in [3] and by A r e n s and J a m e s D u g u n d j i in [4]. This topology was shown in [17] to be the proper setting to study sequences of functions which converge uniformly on compact subsets. But soon, it also turned out to be a natural and interesting locally convex topology on C(X) from the measure-theoretic viewpoint.…”

The Generalized Pre-Open Compact Topology on Function Spaces

“…Arens [3], and Arens and Dugundji [4] developed basic theory of compact-open topology. In 1952, Jackson [8] compared several topologies on function spaces and studied sequences of functions which converge uniformly on compact subset.…”