Linearly Ordered Collections and Paracompactness
نویسندگان
چکیده
منابع مشابه
Linearly Ordered Topological Spaces
This work is devoted to the study of certain cardinality modifications of paracompactness and compactness in the setting of linearly ordered spaces. Some of the concepts treated here have previously been studied by Aquaro [l]1, Gulden [4], Kennison [5], Mansfield [6], Morita [7], and Poppe [9]. On the other hand, the concept of m-boundedness, introduced in §2, is new. Our main results (Theorems...
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a) X is strongly paracompact; b) X is paracompact; c) X is metacompact; d) X is weakly θ-refinable; e) Every open cover of X has a point-countable open refinement; f) X is subparacompact; g) If C is a closed subspace of X, then there are discrete closed sets S and T which are, respectively, well-ordered and reverse-well-ordered by the given ordering of X, have S ∪ T ⊂ C, and have the property t...
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A generate and test algorithm is described which parses a surface form into one or more lexical entries using linearly ordered phonological rules. This algorithm avoids the exponential expansion of search space which a naive parsing algorithm would face by encoding into the form being parsed the ambiguities which arise during parsing. The algorithm has been implemented and tested on real langua...
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The extended answer set semantics for logic programs allows for the defeat of rules to resolve contradictions. We propose a refinement of these semantics based on a preference relation on extended literals. This relation, a strict partial order, induces a partial order on extended answer sets. The preferred answer sets, i.e. those that are minimal w.r.t. the induced order, represent the solutio...
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We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodým compact space is Radon-Nikodým, providing a new partial answer to the problem of continuous images of Radon-Nikodým compacta. It is an open problem posed by Namioka [8] whether the class of Radon-Nikodým...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.2307/2036725