Finite products of filters that are compact relative to a class of filters

Authors

  • Francis Jordan Georgia Southern University
  • Iwo Labuda University of Mississippi
  • Frédéric Mynard Georgia Southern University

DOI:

https://doi.org/10.4995/agt.2007.1878

Keywords:

Compact, Countably compact, Filters, Product space, Product filters

Abstract

Filters whose product with every countable based countably compact filter is countably compact are characterized.

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Author Biographies

Francis Jordan, Georgia Southern University

Dept. Mathematical Sciences

Iwo Labuda, University of Mississippi

Department of Mathematics

Frédéric Mynard, Georgia Southern University

Dept. Mathematical Sciences

References

S. Dolecki, Active boundaries of upper semicontinuous and compactoid relations; closed and inductively perfect maps, Rostock. Math. Coll. 54 (2000), 51–68.

Z. Frolík, The topological product of two pseudocompact spaces, Czech. Math. J. 85 (1960), no. 10, 339–349.

L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, 1960. http://dx.doi.org/10.1007/978-1-4615-7819-2

F. Jordan and F. Mynard, Espaces productivement de Fréchet, C. R. Acad. Sci. Paris, Ser I 335 (2002), 259–262.

F. Jordan and F. Mynard, Productively Fréchet spaces, Czech. Math. J. 54 (2004), no. 129, 981–990.

F. Jordan and F. Mynard , Compatible relations on filters and stability of local topological properties under supremum and product, Top. Appl. 153 (2006), 2386–2412. http://dx.doi.org/10.1016/j.topol.2005.08.008

J. Kelley, General topology, Van Nostrand, 1955.

E. Michael, A quintuple quotient quest, Gen. Topology Appl. 2 (1972), 91–138. http://dx.doi.org/10.1016/0016-660X(72)90040-2

F. Mynard, Products of compact filters and applications to classical product theorems, Top. Appl. 154 (2007), no. 4, 953–958.

F. Mynard, Relations that preserve compact filters, Applied Gen. Top. 8 (2007),171–185.

J. Vaughan, Products of topological spaces, Gen. Topology Appl. 8 (1978), 207–217. http://dx.doi.org/10.1016/0016-660X(78)90001-6

J. E. Vaughan, Countably compact and sequentially compact spaces, vol. Handbook of set-theoretic Topology, pp. 569–602, Elsevier Science, 1984.

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How to Cite

[1]
F. Jordan, I. Labuda, and F. Mynard, “Finite products of filters that are compact relative to a class of filters”, Appl. Gen. Topol., vol. 8, no. 2, pp. 161–170, Oct. 2007.

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Regular Articles