Form Classes

Form equivalence class Howard-Rubin Number: 94

Statement:

For all \(A\subseteq{\Bbb R}\), \(x\in A\) and \(f: A\rightarrow{\Bbb R}\) the following are equivalent:

  1. \((\forall\epsilon>0)(\exists\delta>0)(\forall y\in A)(|y - x| <\delta\)  implies \(|f(y) - f(x)|<\epsilon)\)
  2. Whenever \(\{x_{n}\}\subseteq A\)and \(\lim_{}x_{n} = x\) then \(\lim_{}f(x_{n}) = f(x)\).
Note 5.

Howard-Rubin number: 94 O

Citations (articles): Herrlich/Strekcer [1997] When is \(\Bbb N\) Lindelöf

Connections (notes):

References (books):

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