Geodesic
The Characterization of a Lattice Homomorphism
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 172-175

Voir la notice de l'article provenant de la source Cambridge University Press

We shall give a simple characterization of a lattice homomorphism from a linear lattice E to a linear lattice F. This paper is motivated by the following two theorems in Kaplan [2] :If φ is a lattice homomorphism, then φt(Fb) is an ideal in Eb.(2) If φ is a lattice homomorphism, then φtt is a lattice homomorphism from φbb into φbb.The main theorem is stated and proved in section 3. In section 1, we shall give notations and in section 2, we shall prove a main lemma. For details, we refer to Vulikh [3]. 
Kim, Jongsik. The Characterization of a Lattice Homomorphism. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 172-175. doi: 10.4153/CJM-1975-022-4
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[1] 1. Kaplan, S., The second dual of the space of continuous functions. II, Trans. Amer. Math. Soc. 93 (1959), 329–350. Google Scholar

[2] 2. Kaplan, S., The second dual of the space of continuous functions. V, Trans. Amer. Math. Soc. 118 (1964), 512–546. Google Scholar

[3] 3. Vulikh, B., Introduction to the theory of partially ordered spaces (Wolters-Noordhoff Scientific Pub. Ltd., 1967). Google Scholar

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