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Extension of Lattice Homomorphisms
Author(s) -
Schmidt Garfield C.
Publication year - 1974
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-8.4.707
Subject(s) - infimum and supremum , homomorphism , mathematics , lattice (music) , pure mathematics , unit sphere , extension (predicate logic) , combinatorics , discrete mathematics , physics , computer science , programming language , acoustics
In this paper we prove that a lattice homomorphism f 0 defined on a linear sublattice E of a linear lattice X and dominated there by an M ‐seminorm can be extended to a lattice homomorphism f on X with the supremum of f on the unit ball D the same as the supremum of f 0 on D ∩ E . This result is then used to prove the representation theorems of Jameson and Kakutani which demonstrates its utility in topological M ‐space theory.