Original Articles

A NOTE ON RECONSTRUCTION OF SPACES AND MAPS FROM LATTICE DATA

Published in: Quaestiones Mathematicae
Volume 24 , issue 1 , 2001 , pages: 55–63

DOI: 10.1080/16073606.2001.9639773

Author(s): A. Pultr Department of Applied Mathematics, MFF, , A. Tozzi Dipartimento di Matematica Pura ed Applicata,

Keywords: 54D10 , 06D99

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Abstract

Reconstruction of topological spaces from the lattices Ω(X) of open sets, and of continuous maps from lattice homomorphisms satisfying additional properties (formulated in lattice terms) is discussed. We focus on the question when and how the filters λ(x) = {U | x ε U ε (X)} can be specified by algebraic means.

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