Continuously generated fixed points in P ω 1

Abstract

In this paper we investigate the fixed points of functions that can be obtained by continuous fixed point operators in $\mathit{P}\mathit{\omega }$ . We also introduce an operator Cgn that generates all of these fixed points for any continuous function. In the last two sections of the paper we study the fixed points of $\mathit{\lambda }\mathit{a}.\mathit{a}\circ \mathit{a}$ (retracts) and of $\mathit{\lambda }\mathit{y}$ $\mathit{\lambda }\mathit{f}.\mathit{f}\mathrm{(}\mathrm{(}\mathit{y}\mathrm{)}\mathrm{(}\mathit{f}\mathrm{)}\mathrm{)}$ (fixed point operators).