منابع مشابه
Combinatorics of open covers (VIII)∗
For each space, Ufin(Γ,Ω) is equivalent to Sfin(Ω,O) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindelöf space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Contin...
متن کاملThe combinatorics of open covers (II)
We continue to investigate various diagonalization properties for sequences of open covers of separable metrizable spaces introduced in Part I. These properties generalize classical ones of Rothberger, Menger, Hurewicz, and Gerlits-Nagy. In particular, we show that most of the properties introduced in Part I are indeed distinct. We characterize two of the new properties by showing that they are...
متن کاملThe Combinatorics of Borel Covers
In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: (1) Some of the classes which were different for open covers are equal for Borel covers – Section 1; (2) Some Borel classes coincide with classes that have been studi...
متن کاملCombinatorics of Open Covers VI: Selectors for Sequences of Dense Sets
We consider the following two selection principles for topological spaces: Principle 1: For each sequence of dense subsets, there is a sequence of points from the space, the n-th point coming from the n-th dense set, such that this set of points is dense in the space; Principle 2: For each sequence of dense subsets, there is a sequence of finite sets, the n-th a subset of the n-th dense set, su...
متن کاملS ep 2 00 4 THE COMBINATORICS OF τ - COVERS
We solve four out of the six open problems concerning critical cardi-nalities of topological diagonalization properties involving τ-covers, show that the remaining two cardinals are equal, and give a consistency result concerning this remaining cardinal. Consequently, 21 open problems concerning potential implications between these properties are settled. We also give structural results based o...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2004
ISSN: 0166-8641
DOI: 10.1016/j.topol.2003.08.019