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Stratified Lattice-Valued Balanced Neighborhood Topological Groups

Author

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  • JAWAHER AL-MUFARRIJ

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

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.

Suggested Citation

  • Jawaher Al-Mufarrij, 2012. "Stratified Lattice-Valued Balanced Neighborhood Topological Groups," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 153-166.
    • Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:02:n:s1793005712500019
    DOI: 10.1142/S1793005712500019
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