Geodesic
The fixed point set of open mappings on extremally disconnected spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 789-794.

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We give an example of an extremally disconnected compact Hausdorff space with an open continuous selfmap such that the fixed point set is nonvoid and nowhere dense, resp\. that there is exactly one nonisolated fixed point.
Classification : 54G05, 54G20, 54H05, 54H20, 54H25
Keywords: dynamical systems on extremally disconnected spaces; absolute; Ellentuck space 
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     title = {The fixed point set of open mappings on extremally disconnected spaces},
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Thümmel, Egbert. The fixed point set of open mappings on extremally disconnected spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 4, pp. 789-794. http://geodesic.mathdoc.fr/item/CMUC_1994__35_4_a19/