On C-embedded subspaces of the Sorgenfrey plane

Olena karlova

Ayuda

On C-embedded subspaces of the Sorgenfrey plane

Karlova, Olena ^[1]
1. [1] Chernivtsi National University
  
  Chernivtsi National University
  
  Ucrania
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 16, Nº. 1, 2015, págs. 65-74
Idioma: inglés
DOI: 10.4995/agt.2015.3161
Enlaces
- Texto completo
Resumen
- We show that for a subspace $E\subseteq\{(x,-x):x\in\mathbb R\}$ of the Sorgenfrey plane $\mathbb S^2$ the following conditions are equivalent: (i) $E$ is $C$-embedded in $\mathbb S^2$; (ii) $E$ is $C^*$-embedded in $\mathbb S^2$; (iii) $E$ is a countable $G_\delta$-subspace of $\rr$ and (iv) $E$ is a countable functionally closed subspace of $\ss$. We also prove that $\mathbb S^2$ is not a $\delta$-normally separated space.
Referencias bibliográficas
- W.Bade, Two properties of the Sorgenfrey plane, Pacif. J. Math. 51, no. 2 (1974), 349-354. (http://dx.doi.org/10.2140/pjm.1974.51.349)
- R. Blair and A.Hager, Extensions of zero-sets and of real-valued functions, Math. Zeit. 136 (1974), 41-52. (http://dx.doi.org/10.1007/BF01189255)
- G.Debs, Espaces héréditairement de Baire, Fund. Math. 129, no. 3 (1988), 199-206.
- R. Engelking, General Topology. Revised and completed edition. Heldermann Verlag, Berlin (1989).
- L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton (1960). (http://dx.doi.org/10.1007/978-1-4615-7819-2)
- R. Heath and E. Michael, A property of the Sorgenfrey line, Comp. Math. 23, no. 2 (1971), 185-188.
- T. Hoshina and K. Yamazaki, Weak C-embedding and P-embedding, and product spaces, Topology Appl. 125 (2002), 233-247. (http://dx.doi.org/10.1016/S0166-8641(01)00275-9)
- O.Kalenda and J.Spurny, Extending Baire-one functions on topological spaces, Topology Appl. 149 (2005), 195-216. (http://dx.doi.org/10.1016/j.topol.2004.09.007)
- O. Karlova, On $alpha$-embedded sets and extension of mappings, Comment. Math. Univ. Carolin. 54, no. 3 (2013), 377-396.
- J.Mack, Countable paracompactness and weak normality properties, Trans. Amer. Math. Soc. 148 (1970), 265-272. (http://dx.doi.org/10.1090/S0002-9947-1970-0259856-3)
- H. Ohta, Extension properties and the Niemytzki plane, Appl. Gen. Topol. 1, no. 1 (2000), 45-60.
- H. Ohta and K. Yamazaki, Extension problems of real-valued continuous functions, in: ''Open problems in topology II'', E.Pearl...
- J.Saint-Raymond, Jeux topologiques et espaces de Namioka, Proc. Amer. Math. Soc. 87, no. 3 (1983), 409-504. (http://dx.doi.org/10.1090/S0002-9939-1983-0684646-1)
- W.Sierpinski, Sur une propriete topologique des ensembles denombrables denses en soi, Fund. Math. 1 (1920), 11-16.
- Y.Tanaka, On closedness of $C$- and $C^*$-embeddings, Pacif. J. Math. 68, no. 1 (1977), 283-292. (http://dx.doi.org/10.2140/pjm.1977.68.283)
- J. Terasawa, On the zero-dimensionality of some non-normal product spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 11 (1972), 167-174.