Topological spaces and lattices of lower semicontinuous functions

Thornton, M. C.

doi:10.1090/S0002-9947-1973-0320994-0

Topological spaces and lattices of lower semicontinuous functions
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by M. C. Thornton PDF

Trans. Amer. Math. Soc. 181 (1973), 495-506 Request permission

Abstract:

Lower semicontinuous real-valued functions on a space $X$ form a conditionally complete distributive lattice $L(X)$. Those lattices which can be represented as $L(X)$ for some $X$ are characterized algebraically. All spaces producing isomorphic lattices ate determined. The class of spaces which are determined by their function lattices is introduced.

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