The quantitative difference between countable compactness and compactness

Journal of Mathematical Analysis and Applications

Volumn 343, Issue 1, 2008, Pages 479-491

  Angosto, C ^a   Cascales, B ^a  

^a UNIVERSITY OF MURCIA   (Spain)

Author keywords

Cp (X) spaces; Compactness; Countable compactness; Countably K determined spaces; Distances

Indexed keywords

EID: 41449106294     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2008.01.051     Document Type: Article

References (14)

1. Argyros S., Dodos P., and Kanellopoulos V. Tree structures associated to a family of functions. J. Symbolic Logic 70 3 (2005) 681-695 MR MR2155261 (2006e:03065)
2. Arkhangel'skiǐ A.V. Topological Function Spaces. translated from Russian by R.A.M. Hoksbergen. Math. Appl. (Soviet Series) vol. 78 (1992), Kluwer Academic Publishers Group, Dordrecht MR 92i:54022
3. Astala K., and Tylli H.O. Seminorms related to weak compactness and to Tauberian operators. Math. Proc. Cambridge Philos. Soc. 107 2 (1990) 367-375 MR MR1027789 (91b:47016)
4. Benyamini Y., and Lindenstrauss J. Geometric Nonlinear Functional Analysis, vol. 1. Amer. Math. Soc. Colloq. Publ. vol. 48 (2000), Amer. Math. Soc., Providence, RI MR 2001b:46001
5. Cascales B., Marciszewsky W., and Raja M. Distance to spaces of continuous functions. Topology Appl. 153 13 (2006) 2303-2319 MR MR2238732
6. Engelking R. General Topology. translated from Polish. Monogr. Mat. (Math. Monogr.) vol. 60 (1977), PWN-Polish Scientific Publishers, Warsaw MR 58 #18316b
7. Fabian M., Hájek P., Montesinos V., and Zizler V. A quantitative version of Krein's theorem. Rev. Mat. Iberoamericana 21 1 (2005) 237-248 MR MR2155020 (2006b:46011)
8. Floret K. Weakly Compact Sets. Lecture Notes in Math. vol. 801 (1980), Springer-Verlag, Berlin lectures held at S.U.N.Y., Buffalo, in Spring 1978. MR 82b:46001
9. Grothendieck A. Critères de compacité dans les espaces fonctionnels généraux. Amer. J. Math. 74 (1952) 168-186 MR 13,857e
10. Köthe G. Topological Vector Spaces. I. translated from German by D.J.H. Garling. Grundlehren Math. Wiss. vol. 159 (1969), Springer-Verlag, New York MR 40 #1750
11. Kryczka A., and Prus S. Measure of weak noncompactness under complex interpolation. Studia Math. 147 1 (2001) 89-102 MR MR1853479 (2002h:46122)
12. Orihuela J. Pointwise compactness in spaces of continuous functions. J. London Math. Soc. (2) 36 1 (1987) 143-152 MR 88f:46058
13. M. Sánchez, Compacidad, convexidad y distancias en espacios de Banach duales: Extensiones del Teorema de Krein-Smulian, PhD thesis, Universidad Complutense de Madrid, 2007
14. Talagrand M. Espaces de Banach faiblement K-analytiques. Ann. of Math. (2) 110 3 (1979) 407-438 MR 81a:46021