This paper introduces quasicompact-open topology on C(X) and compares this topology with the compact-open topology and the topology of uniform convergence. Then it examines submetrizability, metrizability, separability, and second countability of the quasicompact-open topology on C(X).
In previous papers, various notions of (strongly) closed subobject, (strongly) open subobject, connected and T i , i = 0, 1, 2 objects in a topological category were introduced and compared. The main objective of this paper is to characterize each of these classes of objects in the category of closure spaces as well as to examine how these generalizations are related.
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