Adjunction Spaces of Monotonically Normal Spaces and Spaces Dominated by Monotonically Normal Subsets
نویسندگان
چکیده
منابع مشابه
Kat Etov's Lemma and Monotonically Normal Spaces
An interpolation lemma due to Kat etov is simpliied in order to make it more general and easier to use. Several results are established to illustrate applications of this lemma, including a characterization of monotonically normal spaces and a topology-free insertion theorem. We also prove that a topological space has an order-preserving insertion if and only if it is dominated by a collection ...
متن کاملOrder-like structure of monotonically normal spaces
For a compact monotonically normal space X we prove: (1) X has a dense set of points with a well-ordered neighborhood base (and so X is co-absolute with a compact orderable space); (2) each point of X has a well-ordered neighborhood πbase (answering a question of Arhangel’skii); (3) X is hereditarily paracompact iff X has countable tightness. In the process we introduce weak-tightness, a notion...
متن کاملCompact-calibres of Regular and Monotonically Normal Spaces
A topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp., point-finite) collection of nonempty open sets is countable. It has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every di...
متن کاملMonotonically Compact and Monotonically Lindelöf Spaces
We answer questions of Bennett, Lutzer, and Matveev by showing that any monotonically compact LOTS is metrizable, and any first-countable Lindelöf GO-space is monotoncically Lindelöf. We also show that any compact monotonically Lindelöf space is first-countable, and is metrizable if scattered, and that separable monotonically compact spaces are metrizable.
متن کاملThe β - space Property in Monotonically Normal Spaces and GO - Spaces
In this paper we examine the role of the β-space property (equivalently of the MCM-property) in generalized ordered (GO-)spaces and, more generally, in monotonically normal spaces. We show that a GO-space is metrizable iff it is a β-space with a Gδ-diagonal and iff it is a quasidevelopable β-space. That last assertion is a corollary of a general theorem that any β-space with a σ-point-finite ba...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1983
ISSN: 0002-9939
DOI: 10.2307/2043646