Remarks on the finite derived set property

Angelo Bella

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.


Keywords

Accumulation points; Urysohn spaces; Product; Function spaces

Full Text:

PDF

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.

O. T. Alas and R. G. Wilson, When a compact space is sequentially compact?, preprint.

A. V. Arhangel′skii, "Topological Function Spaces", Kluwer Academic Publishers, Dordrecht (1992)

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.

Abstract Views

1025
Metrics Loading ...

Metrics powered by PLOS ALM


 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Some observations on compact indestructible spaces
Angelo Bella
Topology and its Applications  vol: 160  issue: 13  first page: 1588  year: 2013  
doi: 10.1016/j.topol.2013.06.004



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