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


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    (Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia)


    (Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia)

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    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.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 08 (2012)
    Issue (Month): 03 ()
    Pages: 361-383

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    Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:03:p:361-383

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    Keywords: Lattice-valued topology; fuzzy neighborhood space; lattice-valued topological group; lattice-valued uniformity; level spaces;


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