On \(AE(n)\)-bicompacta and \(n\)-smooth maps. (English. Russian original) Zbl 0873.54020
Sib. Math. J. 33, No. 2, 312-317 (1992); translation from Sib. Mat. Zh. 33, No. 2, 151-156 (1992).
We present certain new characteristics of \(AE(n)\)-bicompacta and \(n\)-smooth maps. The questions which we shall consider here are closely related to the results of A. N. Dranishnikov [Russ. Math. Surv. 39, No. 5, 63-111 (1984); translation from Usp. Mat. Nauk 39, No. 5(239), 55-95 (1984; Zbl 0572.54012)], V. V. Fedorchuk [Trans. Mosc. Math. Soc. 1989, 167-207 (1989); translation from Tr. Mosk. Mat. O.-va 51, 169-207 (1988; Zbl 0679.54008)], and the author [Sov. Math., Dokl. 25, 507-510 (1982); translation from Dokl. Akad. Nauk SSSR 263, 1073-1077 (1982; Zbl 0515.54019)].
MSC:
| 54C55 | Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) |
| 54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |
| 54D30 | Compactness |
| 54F65 | Topological characterizations of particular spaces |
References:
| [1] | A. N. Dranishnikov, ”Absolute extenders in dimension n and a dimension-increasing n-soft map,” Usp. Matem. Nauk,39, No. 5, 55–95 (1984). |
| [2] | V. V. Fedorchuk, ”Multi-valued retractions and characterization of n-soft maps,” Tr. Mosk. Mat. O-va,51, 169–207 (1988). · Zbl 0679.54008 |
| [3] | L. V. Shirokov, ”External characterization of Dugundji spaces and {\(\kappa\)}-metrizable bicompacta,” Dokl. Akad. Nauk SSSR,263, No. 5, 1073–1077 (1982). |
| [4] | P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory [in Russian], Nauka, Moscow (1975). |
| [5] | A. Pechlinskii, ”Topology of limit spaces of uncountable inverse spectra,” Usp. Matem. Nauk,31, No. 5, 191–226 (1976). |
| [6] | E. V. Shchepin, ”Topology of limit spaces of nondenumerable inverse spectra,” Usp. Matem. Nauk,31, No. 5, 191–226 (1976). · Zbl 0356.54026 |
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