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• 作者：W.W. Comfort ; Ivan S. Gotchev ; Luis Recoder-Nú ; ñ ; ez
• 关键词：Stone– ; Č ; ech compactification ; Hewitt realcompactification ; Dieudonné ; topological completion ; ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V1K-4S6GRHF-4&_mathId=mml15&_
• 刊名：Topology and its Applications
• 出版年：2008
• 出版时间：15 October 2008
• 年：2008
• 卷：155
• 期：17-18
• 页码：2188-2195
• 全文大小：152 K

文摘

A subspace Y of a space X is said to be M-embedded in X if every continuous f:Y→Z with Z metrizable extends to a continuous function .

For topological spaces X_i (iI) and JI, set X_J:=∏_iJX_i.

The authors prove a general theorem concerning κ-box topologies and pseudo-(α,κ)-compact spaces, of which the following is a corollary of the special case κ=α=ω.

Theorem

If YX_I and π_J[Y]=X_J for all ≠J[I]^<ω+, and if each X_J, for ≠J[I]^<ω, is Lindelöf, then Y is M-embedded in X_I.

Remark

Several results in Chapter 10 of the book [W.W. Comfort, S. Negrepontis, Chain Conditions in Topology, Cambridge Tracts in Math., vol. 79, Cambridge Univ. Press, 1982] depend on Lemma 10.1, of which the given proof was incomplete. A principal contribution here is to furnish a correct proof, allowing the present authors to verify and unify all the results from Chapter 10 whose status had become questionable, and to extend several of these.