Form Classes

Form equivalence class Howard-Rubin Number: 1

Statement:

Turinici's Fixed Point Theorem:  If \((X,\le)\) is a directed, partially ordered set and \(\tau\) is a topology on \(X\) such that

  1. \((X,\le)\) is upper semicontinuous with respect to \(\tau\),
  2. Every well ordered subset of \((X,\le)\) is convergent as a net,
then every function \(f:X\to X\) such that \(\forall x\in X\),\(x\le f(x)\) has a fixed point.

Howard-Rubin number: 1 AS

Citations (articles): Manka [1988b] Turinici's fixed point theorem and the axiom of choice

Connections (notes): Note [38] Definitions from Manka [1988a] and Manka [1988b]

References (books):

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