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Enriched Lattice-Valued Topological Groups

Author

Listed:
  • 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)

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.

Suggested Citation

  • T. M. G. Ahsanullah & David Gauld & Jawaher Al-Mufarrij & Fawzi Al-Thukair, 2014. "Enriched Lattice-Valued Topological Groups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 27-53.
    • Handle: RePEc:wsi:nmncxx:v:10:y:2014:i:01:n:s1793005714500021
    DOI: 10.1142/S1793005714500021
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