STRATIFIED LATTICE-VALUED BALANCED NEIGHBORHOOD TOPOLOGICAL GROUPS

Jawaher Al-Mufarrij ()
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Jawaher Al-Mufarrij: Department of Mathematics, Women Section, King Saud University, Riyadh 11495, P. O. Box 22452, Saudi Arabia

New Mathematics and Natural Computation (NMNC), 2012, vol. 08, issue 02, 153-166

Abstract: The aim of this article is to introduce the notion of stratified lattice-valued balanced neighborhood topological group. We also introduce the notions of equicontinuity in stratified lattice-valued neighborhood topological space, and uniform equicontinuity in stratified lattice-valued uniform space. We use these notions to characterize stratified lattice-valued neighborhood topological groups. Moreover, introducing the notions of lattice-valued neighborhood open function and lattice-valued uniformly open function, we show that in a stratified lattice-valued neighborhood topological group these notions are equivalent. Finally, we conclude with a characterization of balanced stratified lattice-valued neighborhood topological group in terms of uniform continuity of binary group operation.

Keywords: Lattice-valued neighborhood topological group; lattice-valued uniform space; lattice-valued equicontinuity; lattice-valued uniform equicontinuity; lattice-valued neighborhood open function; lattice-valued uniformly open function (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1142/S1793005712500019

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