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A criterion for local resolvability of a space and the ω-problem

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Abstrakty
EN
The notion of the resolvability of a topological space was introduced by E. Hewitt [8]. Recently it was understood that this notion is also important in the study of ω)-primitives, especially in the case of nonmetrizable spaces. In the present paper a criterion for the resolvability of a topological space at a point ("local resolvability") is given. This criterion, stated in terms of oscillation and quasicontinuity, permits to conclude, for instance, that on irresolvable spaces no positive continuous real-valued function has an ω-primitive. The result is strenghtened in the case of SI-spaces. It is also shown that every non- negative upper semicontinuous function on a resolvable Baire space has an ω)-primitive.
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Rocznik
Strony
83--96
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
  • Pedagogical University. Institute of Mathematics, Arciszewskiego 22B, 76-200 Słupsk, Poland, stapon@pap.edu.pl
Bibliografia
  • [1] Comfort, W. W., Edwin Hewitt as topologist: An appreciation, Topological Commentatory 6(1) (2001), available at Topology Atlas http://at.yorku.ca/topo1ogy/.
  • [2] Di Bari, C., Vetro, C., Primitive rispetto all'oscillazione, Rend. Circ. Mat. Palermo (2) 51 (2002), 175-178.
  • [3] Duszyński, Z., Grande, Z., Ponomarev, S. P., On the ω-primitive, Math. Slovaca 51(2001), 469-476.
  • [4] Ewert, J., Ponomarev, S. P., Oscillation and ω-primitives, Real Anal. Exchange 26(2) (2001/2002), 687-702.
  • [5] Ewert, J., Ponomarev, S. P., On the existence of ω-primitives on arbitrary metric spaces, Math. Slovaca 53(1) (2003), 51-57.
  • [6] Ewert, J., Ponomarev, S. P., On the convergence of ω-primitives, Math. Slovaca 53(1) (2003), 59-66.
  • [7] Fort, M. K., Jr., Category theorems, Fund. Math. 42 (1955), 276-288.
  • [8] Hewitt, E., A problem of set-theoretic topology, Duke Math. J. 10 (1943), 309-333.
  • [9] Lukes, J., Maly, J., Zajfcek, L.., Fine Topology Methods in Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer-Verlag, Berlin, 1986.
  • [10] Neubrunn, T., Quasi-continuity, Real Anal. Exchange 14 (1988/1989),259-306.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD4-0005-0054
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