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

Francis Jordan, Iwo Labuda, Frédéric Mynard

Abstract

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

Keywords

Compact; Countably compact; Filters; Product space; Product filters

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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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Cited-By (articles included in Crossref)

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1. Products of compact filters and applications to classical product theorems
Frédéric Mynard
Topology and its Applications  vol: 154  issue: 4  first page: 953  year: 2007  
doi: 10.1016/j.topol.2006.09.016



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Universitat Politècnica de València

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