Relations that preserve compact filters

Authors

  • Frédéric Mynard Georgia Southern University

DOI:

https://doi.org/10.4995/agt.2007.1879

Abstract

Many classes of maps are characterized as (possibly multi-valued) maps preserving particular types of compact filters.

Downloads

Download data is not yet available.

Author Biography

Frédéric Mynard, Georgia Southern University

Dept. Mathematical Sciences

References

A. V. Arhangel'skii, Bisequential spaces, tightness of products, and metrizability conditions in topological groups, Trans. Moscow Math. Soc. 55 (1994), 207–219.

B. Cascales and L. Oncina, Compactoid filters and USCO maps, Math. Analysis and Appl. 282 (2003), 826–845. http://dx.doi.org/10.1016/S0022-247X(03)00280-4

C. H. Cook and H. R. Fischer, Regular convergence spaces, Math. Ann. 174 (1967), 1–7. http://dx.doi.org/10.1007/BF01363119

S. Dolecki, Convergence-theoretic methods in quotient quest, Topology Appl. 73 (1996), 1–21. http://dx.doi.org/10.1016/0166-8641(96)00067-3

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

S. Dolecki, Convergence-theoretic characterizations of compactness, Topology Appl. 125 (2002), 393–417. http://dx.doi.org/10.1016/S0166-8641(01)00283-8

S. Dolecki, G. H. Greco, and A. Lechicki, Compactoid and compact filters, Pacific J. Math. 117 (1985), 69–98. http://dx.doi.org/10.2140/pjm.1985.117.69

S. Dolecki, G. H. Greco, and A. Lechicki, When do the upper Kuratowski topology (homeomorphically, Scott topology) and the cocompact topology coincide?, Trans. Amer. Math. Soc. 347 (1995), 2869–2884. http://dx.doi.org/10.1090/S0002-9947-1995-1303118-7

S. Dolecki and F. Mynard, Cascades and multifilters, Topology Appl. 104 (2000), 53–65. [10] Z. Frolík, The topological product of two pseudocompact spaces, Czech. Math. J. 85 (1960), no. 10, 339–349.

Z. Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87–91. http://dx.doi.org/10.1090/S0002-9904-1967-11653-7

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

H. J. Kowalsky, Limesräume und Kompletierung, Math. Nach. 12 (1954), 302–340. http://dx.doi.org/10.1002/mana.19540120504

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, Topology Appl. 154, no. 4 (2007), 953–968. http://dx.doi.org/10.1016/j.topol.2006.09.016

B. J. Pettis, Cluster sets of nets, Proc. Amer. Math. Soc. 22 (1969), 386–391. http://dx.doi.org/10.1090/S0002-9939-1969-0276922-4

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, Total nets and filters, Topology (Proc. Ninth Annual Spring Topology Conf., Memphis State Univ., Memphis, Tenn., 1975), Lecture Notes in Pure and Appl. Math., Vol. 24 (New York), Dekker, 1976, pp. 259–265.

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

Downloads

How to Cite

[1]
F. Mynard, “Relations that preserve compact filters”, Appl. Gen. Topol., vol. 8, no. 2, pp. 171–185, Oct. 2007.

Issue

Section

Regular Articles