On the Lindelöf property of spaces of continuous functions over a Tychonoff space and its subspaces
Oleg Okunev (2009)
Commentationes Mathematicae Universitatis Carolinae
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We study relations between the Lindelöf property in the spaces of continuous functions with the topology of pointwise convergence over a Tychonoff space and over its subspaces. We prove, in particular, the following: a) if is Lindelöf, , and the point has countable character in , then is Lindelöf; b) if is a cozero subspace of a Tychonoff space , then and .