The Cech number of Cp(X) when X is an ordinal space

Authors

  • Ofelia T. Alas Universidade de Sao Paulo
  • Ángel Tamariz-Mascarúa Universidad Nacional Autónoma de México

DOI:

https://doi.org/10.4995/agt.2008.1870

Keywords:

Spaces of continuous functions, Topology of pointwise convergence, Cech number, Ordinal space

Abstract

The Cech number of a space Z, C(Z), is the pseudocharacter of Z in βZ. In this article we obtain, in ZFC and assuming SCH, some upper and lower bounds of the  Cech number of spaces Cp(X) of realvalued continuous functions defined on an ordinal space X with the pointwise convergence topology.

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Author Biography

Ángel Tamariz-Mascarúa, Universidad Nacional Autónoma de México

Departamento de Matemáticas, Facultad de Ciencias

References

O. T. Alas and A. Tamariz-Mascarúa, On the Cech number of Cp(X), II Q & A in General Topology 24 (2006), 31–49.

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E. van Douwen, The integers and topology, in Handbook of Set-Theoretic Topology, North-Holland, 1984, Amsterdam–New-York–Oxford, 111–167.

R. Engelking, General topology, PWN, Warszawa, 1977.

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D. J. Lutzer and R. A. McCoy, Category in function spaces, I, Pacific J. Math. 90 (1980), 145–168. http://dx.doi.org/10.2140/pjm.1980.90.145

O. Okunev and A. Tamariz-Mascarúa, On theCech number of Cp(X), Topology Appl. 137 (2004), 237–249. http://dx.doi.org/10.1016/S0166-8641(03)00213-X

V. V. Tkachuk, Decomposition of Cp(X) into a countable union of subspaces with “good” properties implies “good” properties of Cp(X), Trans. Moscow Math. Soc. 55 (1994), 239–248.

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How to Cite

[1]
O. T. Alas and Ángel Tamariz-Mascarúa, “The Cech number of Cp(X) when X is an ordinal space”, Appl. Gen. Topol., vol. 9, no. 1, pp. 67–76, Apr. 2008.

Issue

Section

Regular Articles