The fixed point set of open mappings on extremally disconnected spaces

Egbert Thümmel

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 4, page 789-794
  • ISSN: 0010-2628

Abstract

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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, respṫhat there is exactly one nonisolated fixed point.

How to cite

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Thümmel, Egbert. "The fixed point set of open mappings on extremally disconnected spaces." Commentationes Mathematicae Universitatis Carolinae 35.4 (1994): 789-794. <http://eudml.org/doc/247592>.

@article{Thümmel1994,
abstract = {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, respṫhat there is exactly one nonisolated fixed point.},
author = {Thümmel, Egbert},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {dynamical systems on extremally disconnected spaces; absolute; Ellentuck space; extremally disconnected compact Hausdorff space; fixed point set; nonisolated fixed point},
language = {eng},
number = {4},
pages = {789-794},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The fixed point set of open mappings on extremally disconnected spaces},
url = {http://eudml.org/doc/247592},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Thümmel, Egbert
TI - The fixed point set of open mappings on extremally disconnected spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 4
SP - 789
EP - 794
AB - 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, respṫhat there is exactly one nonisolated fixed point.
LA - eng
KW - dynamical systems on extremally disconnected spaces; absolute; Ellentuck space; extremally disconnected compact Hausdorff space; fixed point set; nonisolated fixed point
UR - http://eudml.org/doc/247592
ER -

References

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  1. Abramovich Y.A., Arenson E.L., Kitover A.K., Banach C ( K ) -modules and operators preserving disjointness, Longman 1992. Zbl0795.47024MR1202880
  2. Błaszczyk A., Kim Dok Yong, A topological version of a combinatorical theorem of Katětov, Comment. Math. Univ. Carolinae 29 (1988), 657-663. (1988) MR0982783
  3. Comfort W.W., Negrepontis S., The Theory of Ultrafilters, Springer (1974). (1974) Zbl0298.02004MR0396267
  4. Ellentuck E., A new proof that analytic sets are Ramsey, J. Symbolic Logic 39 (1974), 163-165. (1974) Zbl0292.02054MR0349393
  5. 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) MR0233343
  6. Krawczyk A., Steprāns J., Continuous colourings of closed graphs, Topology Appl. 51 (1993), 13-26. (1993) MR1229497
  7. Vermeer J., Fixed-points sets of continuous functions on extremally disconnected spaces, preprint. 

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