Geodesic
Homomorphisms Between Lattices of Zero-Sets
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 1-5

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DOI

For a completely regular Hausdorff topological space X, let Z(X) denote the lattice of zero-sets of X. If T is a continuous map from X to Y, then there is a lattice homomorphism T” from Z(Y) to Z(X) induced by T which is defined by τ‘(A) = τ←(A). A characterization is given of those lattice homomorphisms from Z(Y) to Z(X) which are induced in the above way by a continuous function from X to Y.
DOI : 10.4153/CMB-1978-001-1
Mots-clés : 54C05, 54C50, 54D35, 54D60, zero-set lattice, lattice homomorphism, z-ultrafilter, realcompact, Stone-Cech compactification 
Broverman, S. Homomorphisms Between Lattices of Zero-Sets. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 1-5. doi: 10.4153/CMB-1978-001-1
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