Form Classes

Form equivalence class Howard-Rubin Number: 94

Statement:

\((\forall f: \Bbb R\rightarrow{\Bbb R})(\forall x\in{\Bbb R})\) the following are equivalent:

  1. \((\forall\epsilon > 0)(\exists\delta >0)((\forall y\in\Bbb R)(|y - x|<\delta\rightarrow |f(y) - f(x)|<\epsilon)\).
  2. Whenever \(\lim_{}x_{n} = x\), then\(\lim_{}f(x_{n})=f(x)\).
(A real valued function on \(\Bbb R\) is continuous if and only if it is  sequentially  continuous.)

Howard-Rubin number: 94 P

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):

References (books): Book: Naive Mengen und Abstracte Zahlen, Band III, Felscher, [1979]

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