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On some forms of embeddings of topological spaces. (English. Russian original) Zbl 0632.54009

Russ. Math. Surv. 42, No. 2, 297-298 (1987); translation from Usp. Mat. Nauk 42, No. 2(254), 253-254 (1987).
V. V. Fedorchuk has shown [Usp. Mat. Nauk 37, No.4(226), 187-188 (1982; Zbl 0519.54005)] the class of MAR-compact Hausdorff spaces coincides with the class of AE-1-compact Hausdorff spaces. One of the problems considered here is the characterization of embeddings of AE-1- compact Hausdorff spaces in Tikhonov cubes. Theorem 1. For a compact Hausdorff space X the following conditions are equivalent: (1) \(X\in AE\)- 1 (AE-1 is the class of absolute extensors for normal spaces of dimension \(\leq 1)\); (2) any embedding of X in the Tikhonov cube \(I^{\tau}\) is exponential.

MSC:

54C25 Embedding
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.)

Citations:

Zbl 0519.54005
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