The Selectively Pseudocompact-Open Topology on C(X)

Bulletin of the Iranian Mathematical Society - Tập 47 - Trang 1611-1628 - 2020
Juan Alberto Martínez-Cadena1, Ángel Tamariz-Mascarúa1
1Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México, México

Tóm tắt

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.

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