Form equivalence class Howard-Rubin Number: 1
Statement:
Assume \(P\) is a partially ordered set in which every non-empty chain has an upper bound and \(f: P\to P\) satisfies \(\forall x\in f(P) \cup \{\,a\in P : a\) is an upper bound for some chain in \(f(P)\,\}\),\(x\le f(f(x))\). Then \(f\) has a fixed apex \(u\) (that is, there is some \(v\in P\) such that \(f(u)=v\) and \(f(v)=u\).)
Howard-Rubin number: 1 BC
Citations (articles):
Taskovi'c [1988]
Characterizations of inductive posets with applications
Taskovi'c [1992a]
"The axiom of choice, fixed point theorems and inductive ordered sets"
Connections (notes):
References (books):
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