Connected metrizable subtopologies and partitions into copies of the Cantor set

Authors

  • Irina Druzhinina Universidad Autónoma Metropolitana

DOI:

https://doi.org/10.4995/agt.2006.1919

Keywords:

Metrizable space, Completely metrizable space, Condensation, Connected metrizable subtopology, Cantor set, Zero-dimensional space, Martin’s Axiom

Abstract

We prove under Martin’s Axiom that every separable metrizable space represented as the union of less than 2 ω zero-dimensional compact subsets is zero-dimensional. On the other hand, we show in ZFC that every separable completely metrizable space without isolated points is the union of 2ω pairwise disjoint copies of the Cantor set.

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Author Biography

Irina Druzhinina, Universidad Autónoma Metropolitana

Departamento de Matemáticas

References

A.V. Arhangel’skii and V. I. Ponomarev, Fundamentals of General Topology: Problems and Exercises (Translated from the Russian), Mathematics and its Applications, D. Reidel Publishing Co., Dordrecht, 1984. xvi+415 pp.

R. Engelking, General Topology, Helderman Verlag, Berlin 1989.

P. Delaney and W. Just, Two remarks on weaker connected topologies, Comment. Math. Univ. Carolin. 40 no. 2 (1999), 327–329.

I. Druzhinina, Condensations onto connected metrizable spaces, Houston J. Math. 30 no. 3, (2004), 751–766.

K. Kunen, Set Theory, North Holland, 1980.

M.G. Tkachenko, V.V. Tkachuk, V. Uspenskij, and R.G. Wilson, In quest of weaker connected topologies, Comment. Math. Univ. Carolin. 37 no. 4 (1996), 825–841.

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How to Cite

[1]
I. Druzhinina, “Connected metrizable subtopologies and partitions into copies of the Cantor set”, Appl. Gen. Topol., vol. 7, no. 2, pp. 139–150, Oct. 2006.

Issue

Section

Regular Articles