Measure-theoretic characterizations of certain topological properties

• Autorzy: Buhagiar D. , Chetcuti E. , Dvurečenskij A.

Identyfikatory

DOI

10.4064/ba53-1-9

• Języki publikacji: EN

Abstrakty

EN

It is shown that Cech completeness, ultracompleteness and local compactness can be denned by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.

Słowa kluczowe

EN

Baire measure; Cech completeness; ultracompleteness; local compactness

PL

miara Baire'a; zupełność Cecha; zwartość lokalna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 1
• Strony: 99--109
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Buhagiar D.

• Department of Mathematics, Faculty of Science, University of Malta, Msida MSD.06, Malta

autor

Chetcuti E.

• Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49 , SK-814 73 Bratislava, Slovakia

autor

Dvurečenskij A.

• Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49 , SK-814 73 Bratislava, Slovakia

Bibliografia

• [1] A. D. Alexandroff, Additive set-functions in abstract spacesל Mat. Sb. 8 (50) (1940), 307-348, 9 (51) (1941), 563-628, 13 (55) (1943), 169-238.
• [2] A. V. Arkhangel’skiĭ, On topological spaces which are complete in the sense of Čech Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1961, no. 2, 37—40 (in Russian).
• [3] D. Buhagiar and I. Yoshioka, Ultracomplete topological spaces, Acta Math. Hungar. 92 (2001), 19—26.
• [4] E. Čech, On bicompact spaces, Ann. of Math. 38 (1937), 823—844.
• [5] J. J. Dijkstra, Measures in topology, Master Thesis, Univ. of Amsterdam, 1977.
• [6] R. Engelking, General Topology. rev. ed., Heldermann, Berlin, 1989.
• [7] M. Fréchet, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo 22 (1906), 1—74.
• [8] Z. Frolik, Generalization of the Gδ -property of complete metric spaces, Czechoslovak Math. J. 10 (1960), 359-379.
• [9] I. Glicksberg, The representation of functionals by integrals, Duke Math. J. 19 (1952), 253-261.
• [10] E. Hewitt, Linear functionals on spaces of continuous functions, Fund. Math. 37 (1950), 161-189.
• [11] W. Moran, The additivity of measures on completely regular spaces, J. London Math. Soc. 43 (1968), 633-639.
• [12] —, Measures and mappings on topological spaces, Proc. London Math. Soc. 19 (1969), 493-508.
• [13] —, Measures on metacompact spaces, ibid. 20 (1970), 507—524.
• [14] J. Nagata, Modem General Topology, 2nd rev. ed., Elsevier, Amsterdam, 1985.
• [15] V. I. Ponomarev and V. V. Tkachuk， The countable character of X in ßX versus the countable character of the diagonal in X x X, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1987, no. 5, 16—19 (in Russian).
• [16] S. Romaguera, On cofinally complete metric spaces, Quest. Answers Gen. Topology 16 (1998), 165-169.
• [17] V. S. Varadarajan, Measures on topological spaces, Amer. Math. Soc. Transl. Ser. II 48 (1965), 161-228.