Spaces having a small diagonal
نویسندگان
چکیده
منابع مشابه
O ct 1 99 9 SPACES HAVING A SMALL DIAGONAL
We obtain several results and examples concerning the general question “When must a space with a small diagonal have a Gδ-diagonal?”. In particular, we show (1) every compact metrizably fibered space with a small diagonal is metrizable; (2) there are consistent examples of regular Lindelöf (even hereditarily Lindelöf) spaces with a small diagonal but no Gδ-diagonal; (3) every first-countable he...
متن کاملMore about Spaces with a Small Diagonal
Hušek defines a space X to have a small diagonal if each uncountable subset of X disjoint from the diagonal, has an uncountable subset whose closure is disjoint from the diagonal. Hušek proved that a compact space of weight ω1 which has a small diagonal, will be metrizable, but it remains an open problem to determine if the weight restriction is necessary. It has been shown to be consistent tha...
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It is a well known open problem if, in ZFC, each compact space with a small diagonal is metrizable. We explore properties of compact spaces with a small diagonal using elementary chains of submodels. We prove that ccc subspaces of such spaces have countable π-weight. We generalize a result of Gruenhage about spaces which are metrizably fibered. Finally we discover that if there is a Luzin set o...
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© Mémoires de la S. M. F., 1972, tous droits réservés. L’accès aux archives de la revue « Mémoires de la S. M. F. » (http:// smf.emath.fr/Publications/Memoires/Presentation.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impress...
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Contents 1. Introduction 1 2. Ergodic theory: some background 4 3. Entropy of dynamical systems: some more background 6 4. Conditional Expectation and Martingale theorems 12 5. Countably generated σ-algebras and Conditional measures 14 6. Leaf-wise Measures, the construction 19 7. Leaf-wise Measures and entropy 37 8. The product structure 61 9. Invariant measures and entropy for higher rank sub...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2002
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(01)00140-7