Form Classes

Form equivalence class Howard-Rubin Number: 94

Statement:

For every \(A\subseteq{\Bbb R}\) and \(x\in{\Bbb R}\)the following definitions are equivalent:

  1. \(x\) is in the closure of \(A\) iff every neighborhood of \(x\)intersects \(A\).
  2. \(x\) is in the closure of \(A\) iff there is a sequence\(\{x_{n}\}\subseteq A\) such that \(\lim_{}x_{n}= x\).
Jech [1973b] p 21. (See [94 S].)

Howard-Rubin number: 94 F

Citations (articles): Sierpiński [1918] L’axiome de M. Zermelo et son rˆole dans la th´eorie des ensembles et l’analyse
Herrlich/Strekcer [1997] When is \(\Bbb N\) Lindelöf

Connections (notes): Note [40] Equivalents of Form 94

References (books): Book: The Axiom of Choice, Jech, [1973b]

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