M -fuzzifying gated amalgamations of M -fuzzifying geometric interval spaces

Abstract

In M-fuzzifying interval spaces, the notion of M-fuzzifying base-point orders is introduced, by which some characterizations of M-fuzzifying geometric (resp. Peano, Pasch) interval spaces are obtained. Then notions of M-fuzzifying gated sets, M-fuzzifying gate maps and M-fuzzifying gated amalgamations are introduced. It is shown that M-fuzzifying gated sets are preserved by M-fuzzifying IP-surjective mappings, and that the M-fuzzifying Peano (resp. Pasch, modular, JHC) property is preserved by M-fuzzifying gated amalgamations. In particular, the M-fuzzifying sand-glass property is also preserved by M-fuzzifying gated amalgamations provided that the corresponding M-fuzzifying gate maps are M-fuzzifying II-mappings.

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