The Selectively Pseudocompact-Open Topology on C(X)

This paper studies the selectively pseudocompact-open topology on the set of the real-valued continuous functions on a Tychonoff space, and compares this topology with the alpha-open topology and the topology of uniform convergence on the elements of alpha where alpha is one of the following: {X}, the finite subsets of X, the compact subsets of X, the countably compact subsets of X, and the pseudocompact subsets of X. Moreover, it also analyzes the almost cc-omega-bounded spaces.