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On The Relationships Between Various Lattice-Valued Topological Groups And Their Uniformities

Author

Listed:
  • 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)

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.

Suggested Citation

  • J. Al-Mufarrij & T. M. G. Ahsanullah, 2012. "On The Relationships Between Various Lattice-Valued Topological Groups And Their Uniformities," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 361-383.
    • Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:03:n:s1793005712500081
    DOI: 10.1142/S1793005712500081
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