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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Lattice-invariant topological properties


Author: P. L. Sharma
Journal: Proc. Amer. Math. Soc. 34 (1972), 565-569
MSC: Primary 54D20
DOI: https://doi.org/10.1090/S0002-9939-1972-0295277-2
MathSciNet review: 0295277
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Abstract: The purpose of this paper is to show that an isomorphism between the lattices of all closed sets of two topological spaces induces an isomorphism on the lattices of their zero-sets. This is achieved by showing that any continuous real-valued function on a space X can be transferred to any space lattice-equivalent to X. Several topological properties are shown to be lattice-invariant.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0295277-2
Keywords: Lattice-equivalent topological spaces, lattice-invariant property, zero sets
Article copyright: © Copyright 1972 American Mathematical Society