Inverse systems of absolute retracts and almost continuity
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- by Vladimir N. Akis PDF
- Proc. Amer. Math. Soc. 95 (1985), 499-502 Request permission
Abstract:
Suppose that $Y$ is the inverse limit of a sequence of absolute retracts such that each bonding map is a retraction. We show that $Y$ is the almost continuous retract of the Hilbert cube. It follows that $Y$, the cone over $Y$, the suspension of $Y$, and the product of $Y$ with any absolute retract must have the fixed point property.References
- Vladimir N. Akis, Fixed point theorems and almost continuity, Fund. Math. 121 (1984), no. 2, 133–142. MR 765329, DOI 10.4064/fm-121-2-133-142
- Karol Borsuk, Theory of retracts, Monografie Matematyczne, Tom 44, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. MR 0216473
- B. D. Garrett, Almost continuous retracts, General topology and modern analysis (Proc. Conf., Univ. California, Riverside, Calif., 1980) Academic Press, New York-London, 1981, pp. 229–238. MR 619046
- W. Holsztyński, Universal mappings and fixed point theorems, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 15 (1967), 433–438 (English, with Russian summary). MR 221493
- Kenneth R. Kellum, Almost continuous images of Peano continua, Topology Appl. 11 (1980), no. 3, 293–296. MR 585274, DOI 10.1016/0166-8641(80)90028-0
- Edwin E. Moise, An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua, Trans. Amer. Math. Soc. 63 (1948), 581–594. MR 25733, DOI 10.1090/S0002-9947-1948-0025733-4
- J. Stallings, Fixed point theorems for connectivity maps, Fund. Math. 47 (1959), 249–263. MR 117710, DOI 10.4064/fm-47-3-249-263
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 499-502
- MSC: Primary 54C10; Secondary 54B25, 54C55, 54H15, 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1985-0806096-9
- MathSciNet review: 806096