| Title:
|
The fixed point set of open mappings on extremally disconnected spaces (English) |
| Author:
|
Thümmel, Egbert |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
4 |
| Year:
|
1994 |
| Pages:
|
789-794 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
dynamical systems on extremally disconnected spaces |
| Keyword:
|
absolute |
| Keyword:
|
Ellentuck space |
| MSC:
|
54G05 |
| MSC:
|
54G20 |
| MSC:
|
54H05 |
| MSC:
|
54H20 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 0854.54035 |
| idMR:
|
MR1321249 |
| . |
| Date available:
|
2009-01-08T18:15:11Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118720 |
| . |
| Reference:
|
[AAK] Abramovich Y.A., Arenson E.L., Kitover A.K.: Banach $C(K)$-modules and operators preserving disjointness.Longman 1992. Zbl 0795.47024, MR 1202880 |
| Reference:
|
[BK] Błaszczyk A., Kim Dok Yong: A topological version of a combinatorical theorem of Katětov.Comment. Math. Univ. Carolinae 29 (1988), 657-663. MR 0982783 |
| Reference:
|
[CN] Comfort W.W., Negrepontis S.: The Theory of Ultrafilters.Springer (1974). Zbl 0298.02004, MR 0396267 |
| Reference:
|
[E] Ellentuck E.: A new proof that analytic sets are Ramsey.J. Symbolic Logic 39 (1974), 163-165. Zbl 0292.02054, MR 0349393 |
| Reference:
|
[F] 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. MR 0233343 |
| Reference:
|
[KS] Krawczyk A., Steprāns J.: Continuous colourings of closed graphs.Topology Appl. 51 (1993), 13-26. MR 1229497 |
| Reference:
|
[V] Vermeer J.: Fixed-points sets of continuous functions on extremally disconnected spaces.preprint. |
| . |
