منابع مشابه
A Screenable, Σ-relatively Discrete Dowker Space
A Dowker space (that is, a normal space that is not countably metacompact) is constructed which is also screenable and the countable union of discrete subspaces. The construction and proofs are easy modifications of the ones for Balogh’s screenable Dowker space [B1]. Balogh’s example is presented alongside the modification in a new exposition with several new results common to the two spaces, i...
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Using results announced by Stevo Todorcevic we establish that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. Modulo the large cardinal, this answers a question of S. Watson. We also solve a problem raised by the second author, proving that it is consistent with ZFC that every first countable hered...
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Let us quickly recall the definitions of the terms which are used in the statement of Theorem 1, and which will be used throughout this paper. Let X be a topological space. A collection <R of subsets of X is called open (resp. closed) if every element of "R. is open (resp. closed) in X. A covering of X is a collection of subsets of X whose union is X; observe that in this paper a covering need ...
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A space X is said to be strongly base-paracompact if there is a basis B for X with |B| = w(X) such that every open cover of X has a star-finite open refinement by members of B. Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions F with cardinality equal to the weight such that every open cover has a l...
متن کاملSeparation in Countably Paracompact Spaces
We study the question "Are discrete families of points separated in countably paracompact spaces?" in the class of first countable spaces and the class of separable spaces. Two of the main directions of research in general topology in the last thirty years have been the work of Jones, Bing, Tall, Fleissner, Nyikos and others motivated by the normal Moore space problem (when are discrete familie...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1983
ISSN: 0166-8641
DOI: 10.1016/0166-8641(83)90061-5