Abstract
This paper is devoted to analyzing the topology of uniform convergence on Lindelöf subspaces of X on the set of real-valued continuous functions from X, C(X). The set C(X) endowed with this topology is denoted by Cl,u(X). We compare this topology with the pointwise convergence topology, the compact-open topology and the uniform convergence topology. Also, we analyze the relations among Cl,u(X), the open-Lindelöf topology on C(X), Cl(X), and the space C(X) with the topology of uniform convergence on countable subsets, Cs(X). Moreover, we determine when Cl,u(X) satisfies some topological properties such as metrizability, separability, countable cellularity, Čech-completeness and the Baire property.
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