Suche Bilder Maps Play YouTube News Gmail Drive Mehr »
Anmelden
Books Bücher
" Prove that a metric space X is separable if and only if there exists a countable collection U of open sets such that every open set in X can be expressed as a union of members of U. "
Real Analysis - Seite 368
von Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson - 1997 - 713 Seiten
Vollansicht - Über dieses Buch

Elements of Functional Analysis

Francis Hirsch, Gilles Lacombe - 1999 - 424 Seiten
...continuous function / : R -> R that has a local extremum at every point is constant. 4. Lindelof's Theorem. Prove that a metric space X is separable if and only if every open cover of X (that is, every family of open sets whose union is X) has a countable subcover...
Eingeschränkte Leseprobe - Über dieses Buch

Elementary Real Analysis, Band 1

Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner - 2008 - 685 Seiten
...(b) Give an example of a metric space and a unit sphere that is not separable. SEE NOTE 335 13.7.9 Prove that a metric space X is separable if and only...exists a countable collection U of open sets such that every open set in X can be expressed as a union of members of U. 13.7.10 Prove that a product of two...
Vollansicht - Über dieses Buch

Elementary Real Analysis

Brian S. Thomson, Judith B. Bruckner, Andrew M. Bruckner - 2001 - 753 Seiten
...metrics di, d2, rfoo(b) Give an example of a metric space and a unit sphere that is not separable. 13.7.9 Prove that a metric space X is separable if and only...exists a countable collection U of open sets such that every open set in X can be expressed as a union of members of U. 13.7.10 Prove that a product of two...
Vollansicht - Über dieses Buch

Elements of Operator Theory

Carlos S. Kubrusly - 2001 - 546 Seiten
...3.46. (b) Separability is a topological invariant. Problem 3.49. Verify the following propositions. (a) A metric space X is separable if and only if there exists a countable subset A of X such that every nonempty open ball centered at each x € X meets A (ie, if and only...
Eingeschränkte Leseprobe - Über dieses Buch




  1. Meine Mediathek
  2. Hilfe
  3. Erweiterte Buchsuche