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Pointwise Compatibility, Lattices of f ‐proximities and Counterexamples
Author(s) -
SRIVASTAVA PRAMILA,
KHARE MONA
Publication year - 1994
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1994.tb44139.x
Subject(s) - pointwise , counterexample , compatibility (geochemistry) , distributive property , mathematics , distributive lattice , lattice (music) , pure mathematics , discrete mathematics , physics , mathematical analysis , materials science , acoustics , composite material
The concept of pointwise compatibility in the family of all basic proximities on a set X is introduced and studied. It is proved that the family of all pointwise compatible f ‐proximities, under suitable restrictions on f , forms a complete distributive lattice. To the known f ‐proximities is added a new proximity, termed as p ‐proximity. Counterexamples are constructed in answer to questions regarding the existing one‐way implications for different f ‐proximities.