Amalgams, connectifications, and homogeneous compacta
نویسندگان
چکیده
منابع مشابه
Amalgams, Connectifications, and Homogeneous Compacta
We construct a path-connected homogenous compactum with cellularity c that is not homeomorphic to any product of dyadic compacta and first countable compacta. We also prove some closure properties for classes of spaces defined by various connectifiability conditions. One application is that every infinite product of infinite topological sums of Ti spaces has a Ti pathwise connectification, wher...
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The Noetherian type of a space is the least κ such that it has a base that is κ-like with respect to reverse inclusion. Just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Noetherian type and related cardinal functions. We prove these and many other results about these cardinal functions. For example, every homogeneous dyadic compactu...
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We prove that if X is a power homogeneous compact space then |X| 2c(X)·πχ(X). This generalizes similar results of Arhangel’skiı̆, van Douwen and Ismail. We apply this result to get new estimates for the cardinality of (power) homogeneous compacta satisfying some special conditions. 2004 Elsevier B.V. All rights reserved.
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Under GCH, k(X) _< ~(X) for every homogeneous compactum X. CH implies that a homogeneous compactum of countable ~r-weight is first countable. There is a compact space of countable 7r-weight and uncountable character which is homogeneous under MA+-~CH, but not under CH.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2007
ISSN: 0166-8641
DOI: 10.1016/j.topol.2006.11.007