Abstract
The space of continuous real-valued functions with set-open topology is studied. The coincidence of the set-open topologies for various families λ is considered and conditions for a set-open topology to coincide with the uniform topology are investigated. The separation axioms in the spaces C λ(X) are studied. Criteria for the local compactness and σ-compactness of C λ(X) are given.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 34, General Topology, 2005.
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Nokhrin, S.E. Some properties of set-open topologies. J Math Sci 144, 4123–4151 (2007). https://doi.org/10.1007/s10958-007-0258-3
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DOI: https://doi.org/10.1007/s10958-007-0258-3