| Title:
|
Pseudo-homotopies of the pseudo-arc (English) |
| Author:
|
Illanes, Alejandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
629-635 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a continuum. Two maps $g,h:X\rightarrow X$ are said to be pseudo-homotopic provided that there exist a continuum $C$, points $s,t\in C$ and a continuous function $H:X\times C\rightarrow X$ such that for each $x\in X$, $H(x,s)=g(x)$ and $H(x,t)=h(x)$. In this paper we prove that if $P$ is the pseudo-arc, $g$ is one-to-one and $h$ is pseudo-homotopic to $g$, then $g=h$. This theorem generalizes previous results by W. Lewis and M. Sobolewski. (English) |
| Keyword:
|
pseudo-arc |
| Keyword:
|
pseudo-contractible |
| Keyword:
|
pseudo-homotopy |
| MSC:
|
54B10 |
| MSC:
|
54F15 |
| MSC:
|
54F50 |
| idMR:
|
MR3016431 |
| . |
| Date available:
|
2013-03-02T13:49:01Z |
| Last updated:
|
2015-02-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143195 |
| . |
| Reference:
|
[1] Chacón-Tirado M.E., Illanes A., Leonel R.: Factorwise rigidity of embeddings of the products of pseudo-arcs.Colloq. Math. 128 (2012), 7–14. 10.4064/cm128-1-2 |
| Reference:
|
[2] Illanes A., Nadler S.B., Jr.: Hyperspaces Fundamentals and Recent Advances.Monographs and Textbooks in Pure and Applied Mathematics, 216, Marcel Dekker, Inc., New York, Basel, 1999. Zbl 0933.54009, MR 1670250 |
| Reference:
|
[3] Holsztyński W.: Universal mappings and fixed point theorems.Bull. Acad. Pol. 15 (1967), 433–438. Zbl 0156.43603, MR 0221493 |
| Reference:
|
[4] Holsztyński W.: Universality of the product mappings into products of $I^{n}$ and snake-like spaces.Fund. Math. 64 (1969), 147–155. MR 0244936 |
| Reference:
|
[5] Kuperberg W.: Continua with the Houston Problem Book.H. Cook, W.T. Ingram, K.T. Kuperberg, A. Lelek and P. Minc (Eds.), Lecture Notes in Pure and Applied Mathematics, 170, Marcel Dekker, New York, 1995, pp. 372–373. Zbl 0813.00008, MR 1326830 |
| Reference:
|
[6] Lewis W.: Pseudo-arcs and connectedness in homeomorphism groups.Proc. Amer. Math. Soc. 87 (1983), no. 4, 745–748. Zbl 0525.54024, MR 0687655, 10.1090/S0002-9939-1983-0687655-1 |
| Reference:
|
[7] Lewis W.: The pseudo-arc.Bol. Soc. Mat. Mexicana (3) 5 (1999), 25–77. Zbl 1211.54047, MR 1692467 |
| Reference:
|
[8] Lewis W.: Indecomposable Continua.Open Problems in Topology II, 304–318, edited by E. Pearl, Elsevier, 2007. Zbl 0890.54009 |
| Reference:
|
[9] Nadler S.B., Jr.: Continuum Theory. An Introduction.Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, New York, 1992. Zbl 0757.54009, MR 1192552 |
| Reference:
|
[10] Sobolewski M.: Pseudo-contractibility of chainable continua.Topology Appl. 154 (2007), 2983–2987. Zbl 1129.54020, MR 2355883, 10.1016/j.topol.2007.06.010 |
| . |
