Three Lowen factors, namely, ω, [ ] and ι, are extended into I-fuzzy topogenous spaces and their properties are studied. Then concepts of induced I-fuzzy topogenous spaces, weakly induced I-fuzzy topogenous spaces and stratified I-fuzzy topogenous spaces are introduced and characterized by Lowen factors. Also, relations among these spaces can also be preserved in their quotient spaces and subspaces.
ChangC.L., Fuzzy topological spaces, J Math Anal Appl24 (1968), 182–190.
2.
CsászárA., Foundations of General topology, Pergamon Press, New York-Oxford, 1963.
3.
HuttonB., Uniformities on fuzzy topological spaces, J Math Anal Appl58 (1977), 559–571.
4.
KatsarasA.K., On fuzzy proximity spaces, J Math Anal Appl75 (1980), 571–583.
5.
KatsarasA.K. and PetalasC.G., On fuzzy syntopogenous structure, J Math Anal Appl99 (1983), 219–236.
6.
KatsarasA.K. and PetalasC.G., A unified theory of fuzzy topologies, fuzzy proximities and fuzzy uniformities, Rev. Roumaine Math Pures Appl28 (1983), 845–856.
7.
KatsarasA.K., Fuzzy syntopogenous structures compatible with Lowen fuzzy uniformities and Artico-Moresco fuzzy proximities, Fuzzy Sets and Systems36 (1990), 357–393.
8.
KhedrF.H., Abd El-HakeimK.M., ZeyadaF.M. and SayedO.R., Fuzzifying proximity and strong fuzzifying uniformity, J Fuzzy Math10 (2002), 97–103.
9.
LiuY.M. and LuoM.C., Fuzzy topology, World Scientific publishing,Singapore, 1997.
10.
LowenR., Fuzzy topological spaces and fuzzy compactness, J Math Anal Appl56 (1976), 621–633.
11.
RamadanA.A., On smooth topological spaces, Fuzzy sets and systems48 (1992), 371–375.
12.
RamadanA.A., Smooth pretopogenous structures, Fuzzy Sets and Systems86 (1997), 381–389.
