Geodesic
Amsterdam Properties of Cp (X) Imply Discreteness of X
Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 570-578

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DOI

We prove, among other things, that if ${{C}_{p}}\left( X \right)$ is subcompact in the sense of de Groot, then the space $X$ is discrete. This generalizes a series of previous results on completeness properties of function spaces.
DOI : 10.4153/CMB-2008-056-9
Mots-clés : 54B10, 54C05, 54D30, regular filterbase, subcompact space, function space, discrete space 
Lutzer, D. J.; Mill, J. van; Tkachuk, V. V. Amsterdam Properties of Cp (X) Imply Discreteness of X. Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 570-578. doi: 10.4153/CMB-2008-056-9
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     title = {Amsterdam {Properties} of {Cp} {(X)} {Imply} {Discreteness} of {X}},
     journal = {Canadian mathematical bulletin},
     pages = {570--578},
     year = {2008},
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     doi = {10.4153/CMB-2008-056-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-056-9/}
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