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Topological spaces and lattices of lower semicontinuous functions. (English) Zbl 0238.54012

##### MSC:
 54C30 Real-valued functions in general topology 54A05 Topological spaces and generalizations (closure spaces, etc.)
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##### References:
 [1] Frank W. Anderson and Robert L. Blair, Characterizations of the algebra of all real-valued continuous functions on a completely regular space, Illinois J. Math. 3 (1959), 121 – 133. · Zbl 0083.17403 [2] C. E. Aull and W. J. Thron, Separation axioms between \?$$_{0}$$ and \?$$_{1}$$, Nederl. Akad. Wetensch. Proc. Ser. A 65 = Indag. Math. 24 (1962), 26 – 37. · Zbl 0108.35402 [3] Tjepke Blanksma, Lattice characterizations of topologies and compactifications, Doctoral dissertation, University of Utrecht, Rijksuniversiteit te Utrecht, Groningen, 1968. · Zbl 0157.53201 [4] David Drake and W. J. Thron, On the representations of an abstract lattice as the family of closed sets of a topological space, Trans. Amer. Math. Soc. 120 (1965), 57 – 71. · Zbl 0132.17702 [5] Louis D. Nel, Lattices of lower semi-continuous functions and associated topological spaces, Pacific J. Math. 40 (1972), 667 – 673. · Zbl 0231.46046 [6] L. D. Nel and R. G. Wilson, Epireflections in the category of \?$$_{0}$$-spaces, Fund. Math. 75 (1972), no. 1, 69 – 74. · Zbl 0232.54018 [7] Ladislav Skula, On a reflective subcategory of the category of all topological spaces., Trans. Amer. Math. Soc. 142 (1969), 37 – 41. · Zbl 0185.50401
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