کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9516885 1633121 2005 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Compatible algebraic structures on scattered compacta
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Compatible algebraic structures on scattered compacta
چکیده انگلیسی
It is proved that each hereditarily collectionwise Hausdorff compact scattered space with finite scattered height admits a continuous semilattice operation turning it into a topological semilattice with open principal filters. On the other hand a compactification γN of a countable discrete space N whose remainder is homeomorphic to [0,ω1] admits no (separately) continuous binary operation turning γN into an inverse semigroup (semilattice). Also we construct a compactification ψN of N admitting no separately continuous semilattice operation and such that the remainder ψN∖N is homeomorphic to the one-point compactification of an uncountable discrete space. To show that ψN admits no continuous semilattice operation we prove that the set of isolated points of a compact scattered topological semilattice X of scattered height 2 is sequentially dense in X. Also we prove that each separable scattered compactum with scattered height 2 is a subspace of a separable compact scattered topological semilattice with open principal filters and scattered height 2. This allows us to construct an example of a separable compact scattered topological semilattice with open principal filters and scattered height 2, which fails to be Fréchet-Urysohn. Also we construct an example of a Fréchet-Urysohn separable non-metrizable compact scattered topological semilattice with open principal filters and scattered height 2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 153, Issues 5–6, 1 December 2005, Pages 710-723
نویسندگان
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