ON THE RELATIONSHIPS BETWEEN VARIOUS LATTICE-VALUED TOPOLOGICAL GROUPS AND THEIR UNIFORMITIES

J. Al-Mufarrij () and T. M. G. Ahsanullah ()
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J. Al-Mufarrij: Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
T. M. G. Ahsanullah: Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

New Mathematics and Natural Computation (NMNC), 2012, vol. 08, issue 03, 361-383

Abstract: The purpose of this article is to investigate the relationships between some of the lattice-valued topological groups, and the lattice-valued uniformities that they inherit. In so doing, we look at the relationship between (a) crisp sets of lattice-valued neighborhood groups and lattice-valued neighborhood topological groups, and their uniformities; (b) lattice-valued topological groups of ordinary subsets and fuzzy neighborhood groups, and their uniformities. We also investigate the connection between stratified lattice-valued neighborhood topological group and its level spaces.

Keywords: Lattice-valued topology; fuzzy neighborhood space; lattice-valued topological group; lattice-valued uniformity; level spaces (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S1793005712500081

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