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- W2078271330 abstract "Let S be a compact topological inverse Clifford semigroup S such that the maximal semilattice E and all maximal groups of S are metrizable. We prove that S is first countable and has countable cellularity; moreover, S is metrizable, provided one of the following conditions is satisfied: (1) (MA+¬CH) holds; (2) E is a G δ -set in S ; (3) E is zero-dimensional; (4) E is a Lawson semilattice; (5) all maximal groups of S are Lie groups; (6) S is dyadic or scadic compact; (7) S is a fragmentable (or Rosenthal) monolithic compactum; (8) S is a Corson (or Rosenthal) compactum with countable spread. Under CH two (separable and unseparable) compact non-metrizable topological inverse commutative semigroups with metrizable subsemilattices and subgroups are constructed. One of these semigroups is a first-countable ccc Corson compact space satisfying the properties ( M ), (∗) and ( K n ) for all n ⩾2 but failing (∗∗) ." @default.
- W2078271330 created "2016-06-24" @default.
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- W2078271330 date "2003-02-01" @default.
- W2078271330 modified "2023-09-28" @default.
- W2078271330 title "On cardinal invariants and metrizability of topological inverse Clifford semigroups" @default.
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- W2078271330 doi "https://doi.org/10.1016/s0166-8641(02)00083-4" @default.
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