Remarks on the finite derived set property

Authors

  • Angelo Bella University of Catania

DOI:

https://doi.org/10.4995/agt.2005.1958

Keywords:

Accumulation points, Urysohn spaces, Product, Function spaces

Abstract

The finite derived set property asserts that any infinite subset of a space has an infinite subset with only finitely many accumulation points. Among other things, we study this property in the case of a function space with the topology of pointwise convergence.

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Author Biography

Angelo Bella, University of Catania

Department of Mathematics

References

O. T. Alas, M. Tkachenko, V. Tkachuk and R. Wilson The FDS-property and the spaces in which compact sets are closed, Sci. Math. Japan, to appear.

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A. Bella and O. Pavlov, Embeddings into pseudocompact spaces of countable tightness, Topology Appl. 138 (2004), 161-166. https://doi.org/10.1016/j.topol.2003.03.001

E. K. van Douwen, "The Integers and Topology", Handbook of Set-theoretic Topology (K.Kunen and J.E. Vaughan Editors), Elsevier Science Publishers B.V., Amsterdam (1984), 111 -167. https://doi.org/10.1016/B978-0-444-86580-9.50006-9

R. Engelking, "General Topology" Heldermann-Verlag, Berlin (1989).

P. Simon, Product of sequentially compact spaces, Rend. Ist. Mat. Univ. Trieste 25 (1994), 447-450.

D. Shakmatov, M. Tkachenko and R. Wilson, Transversal and T1-independent topologies, Houston J. Math. 30 (2004), 421-433.

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How to Cite

[1]
A. Bella, “Remarks on the finite derived set property”, Appl. Gen. Topol., vol. 6, no. 1, pp. 101–106, Apr. 2005.

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