Characterizing topologies by functions
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- by Melvin C. Thornton PDF
- Proc. Amer. Math. Soc. 36 (1972), 613-614 Request permission
Abstract:
The multiplicative structure of the idempotents in the semiring of nonnegative lower semicontinuous functions on a large class of spaces determines the topology of the space.References
- 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. MR 188963, DOI 10.1090/S0002-9947-1965-0188963-7
- R. Nielsen and C. Sloyer, Ideals of semi-continuous functions and compactifications of $T_{1}$ spaces, Math. Ann. 187 (1970), 329–331. MR 273572, DOI 10.1007/BF01396463
- W. J. Thron, Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671–679. MR 146787
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 613-614
- MSC: Primary 54C40
- DOI: https://doi.org/10.1090/S0002-9939-1972-0309055-9
- MathSciNet review: 0309055