Extension properties and the Niemytzki plane

Haruto Ohta


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.


C*-embedded; C-embedded; P-embedded; uniformly locally finite; Niemytzki plane; Tychonoff plank

Subject classification

54C45; 54G20

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1. Products of Weak P ‐Spaces and K ‐Analytic Spaces
Kaori Yamazaki
Mathematika  vol: 54  issue: 1-2  first page: 67  year: 2007  
doi: 10.1112/S002557930000022X

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt