Abstract
The ℝ-compactness property is studied, and criteria are established for the coincidence of the set-open topology and the topology of uniform convergence on the spaces of continuous functions.
Similar content being viewed by others
References
M. O. Asanov, Candidate’s Dissertation in Physics and Mathematics (Sverdlovsk, 1980).
S. E. Nokhrin, Candidate’s Dissertation in Physics and Mathematics (Yekaterinburg, 1997).
R. Engelking, General Topology (PWN, Warsaw, 1977; Mir, Moscow, 1986).
R. Arens and J. Dugundji, Pac. J. Math. 1, 5 (1951).
R. H. Fox, Bull. Amer. Math. Soc. 51, 429 (1945).
R. A. McCoy and I. Ntantu, Topological Properties of Spaces of Continuous Functions (Springer-Verlag, Berlin, 1988).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.E. Nokhrin, A.V. Osipov, 2009, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Vol. 15, No. 2.
Rights and permissions
About this article
Cite this article
Nokhrin, S.E., Osipov, A.V. On the coincidence of set-open and uniform topologies. Proc. Steklov Inst. Math. 267 (Suppl 1), 184–191 (2009). https://doi.org/10.1134/S0081543809070165
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0081543809070165