Geodesic
Spaces of continuous characteristic functions
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 599-608.

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We show that if $X$ is first-countable, of countable extent, and a subspace of some ordinal, then $C_p(X,2)$ is Lindelöf.
Classification : 54C35, 54D20, 54F05
Keywords: $C_p(X, Y)$; subspace of ordinals; countable extent; Lindel" of space 
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Buzyakova, Raushan Z. Spaces of continuous characteristic functions. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 599-608. http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a4/