ENRICHED LATTICE-VALUED TOPOLOGICAL GROUPS

T. M. G. Ahsanullah (), David Gauld (), Jawaher Al-Mufarrij () and Fawzi Al-Thukair ()
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T. M. G. Ahsanullah: Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
David Gauld: Department of Mathematics, Auckland University, Auckland, New Zealand
Jawaher Al-Mufarrij: Department of Mathematics, College of Science, Women Section, King Saud University, Riyadh 11491, Saudi Arabia
Fawzi Al-Thukair: Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

New Mathematics and Natural Computation (NMNC), 2014, vol. 10, issue 01, 27-53

Abstract: In this paper, we focus on enrichedcl-premonoid-valued topological groups, and their so-calledchange-of-basis lattice. In so doing, we takeLas an enrichedcl-premonoid and present a categorySL-NTopGrp, of stratified enrichedcl-premonoid-valued neighborhood topological groups. We produce some characterization theorems, and prove that every stratifiedL-neighborhood topological group is uniformizable. Finally, we look at the enriched lattice-valued neighborhood topological group when the underlying basis is changed under certain functorial mechanism.

Keywords: L-neighborhood topological group; L-uniform space; L-subgroup of a group; change-of-basis lattice (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S1793005714500021

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