The fixed point set of open mappings on extremally disconnected spaces
Thümmel, Egbert
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 789-794 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1994-01-01
Classification:  54G05,  54G20,  54H05,  54H20,  54H25
@article{118720,
     author = {Egbert Th\"ummel},
     title = {The fixed point set of open mappings on extremally disconnected spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {789-794},
     zbl = {0854.54035},
     mrnumber = {1321249},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118720}
}
Thümmel, Egbert. The fixed point set of open mappings on extremally disconnected spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 789-794. http://gdmltest.u-ga.fr/item/118720/

Abramovich Y.A.; Arenson E.L.; Kitover A.K. Banach $C(K)$-modules and operators preserving disjointness, Longman 1992. | MR 1202880 | Zbl 0795.47024

Błaszczyk A.; Kim Dok Yong A topological version of a combinatorical theorem of Katětov, Comment. Math. Univ. Carolinae 29 (1988), 657-663. (1988) | MR 0982783

Comfort W.W.; Negrepontis S. The Theory of Ultrafilters, Springer (1974). (1974) | MR 0396267 | Zbl 0298.02004

Ellentuck E. A new proof that analytic sets are Ramsey, J. Symbolic Logic 39 (1974), 163-165. (1974) | MR 0349393 | Zbl 0292.02054

Frolík Z Fixed points of maps of extremally disconnected spaces and complete Boolean algebras, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 16 (1968), 269-275. (1968) | MR 0233343

Krawczyk A.; Steprāns J. Continuous colourings of closed graphs, Topology Appl. 51 (1993), 13-26. (1993) | MR 1229497

Vermeer J. Fixed-points sets of continuous functions on extremally disconnected spaces, preprint.