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
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
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,Ï1] admits no (separately) continuous binary operation turning γN into an inverse semigroup (semilattice). Also we construct a compactification ÏN of N admitting no separately continuous semilattice operation and such that the remainder ÏNâN is homeomorphic to the one-point compactification of an uncountable discrete space. To show that ÏN 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 5â6, 1 December 2005, Pages 710-723
Journal: Topology and its Applications - Volume 153, Issues 5â6, 1 December 2005, Pages 710-723
نویسندگان
Taras Banakh, Oleg V. Gutik, M. Rajagopalan,