Extension properties and the Niemytzki plane

[EN] The first part of the paper is a brief survey on recent topics concerning the relationship between C*-embedding and C-embedding for closed subsets. The second part studies extension properties of the Niemytzki plane NO. A zero-set, z-; C*-, and P-embedded subsets of NP are determined. Finally, we prove that every C*-embedded subset of NP is a P-embedded zero-set, which answers a problem raised in the first part.Ohta, H. (2000). Extension properties and the Niemytzki plane. Applied General Topology. 1(1):45-60. doi:10.4995/agt.2000.3023.SWORD45601

Local compactness and Hewitt realcompactifications of products II

AbstractWe generalize and refine results from the author's paper [18]. For a completely regular Hausdorff space X, υX denotes the Hewitt realcompactification of X. It is proved that if υ(X×Y)=υX×υY for any metacompact subparacompact (or m-paracompact) space Y, then X is locally compact. A P(n)-space is a space in which every intersection of less than n open sets is open. A characterization of those spaces X such that υ (X×Y = υX×υY for any (metacompact) P(n)-space Y is also obtained

位相空間の次元を変えるk-先導と写像

For a Tychonoff space X, let kX be the k-leader of X, dim X the covering dimension of X and Ind X the large inductive dimension of X. We prove: (1) For every n = 1,2,3,...,∞, there exists a regular Lindelof space X such that kX ix normal and dim X = Ind X = 0 ω1, then for every n = 1,2,3,...,∞, there exists an open and closed, continuous map f from a normal space X onto a normal space Y such that dim f^-1 (y) = Ind f^-1 (y) = 0 for each y∊Y and dim X = n > 0 = dim Y = Ind Y

Does C* -embedding imply C*-embedding in the realm of products with a non-discrete metric factor?

The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's

Elementary Submodel Arguments in Balogh\u27s Dowker Spaces

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