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Abstrakty
Let x_0 be a q-point of a regular space X, Y a Hausdorff space whose relatively countably compact subsets are relatively compact and let F:X=>Y be an upper semicontinuous set valued map. Then the active boundary Frac F(x_0) is the smallest compact kernel of F at x_0.
Wydawca
Rocznik
Tom
Strony
225--235
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Department of Mathematics, The University of Mississippi, mmlabuda@olemiss.edu
Bibliografia
- [1] G. Beer, Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers 1993.
- [2] J. Cao, W. Moors and I. Reilly, On the Choquet-Dolecki Theorem, J. Math. Anal. Appl. 234 (1999), 1-5.
- [3] J. Cao, W. Moors and I. Reilly, Topological properties defined by games and their applications, Topology Appl. 123 (2002), 47-55.
- [4] G. Choquet, Convergences, Ann.Univ.Grenoble 23 (1948), 57-112.
- [5] S. Dolecki, Remarks on semicontinuity, Bull.Acad.Polon.Sci.,Sér.Sci.Math. 25 (1977), 863- 867.
- [6] S. Dolecki, Semicontinuity in constrained optimization II, Control Cybernet. 7(2) (1978), 5-16.
- [7] S. Dolecki, Active boundaries of upper semicontinuous and compactoid relations; closed and inductively perfect maps, Rostock Math. Kolloq. 54 (2000), 51-68.
- [8] S. Dolecki and A. Lechicki, On structure of upper semicontinuity, J.Math.Anal.Appl. 88 (1982), 547-554.
- [9] S. Dolecki and S. Rolewicz, Metric characterization of upper semicontinuity, J.Math. Anal.Appl. 69 (1979), 146-152.
- [10] L. Drewnowski, I. Labuda, On minimal upper semicontinuous compact-valued maps, Rocky Mountain J. Math. 20 (1990), 1-16.
- [11] R. Hansell, J. Jayne, I. Labuda and C. A. Rogers, Boundaries of and selectors for upper semicontinuous multi-valued maps, Math. Z. 189 (1985), 297-318.
- [12] J. Kelley, General Topology, Van Nostrand 1955.
- [13] I. Labuda, On a theorem of Choquet and Dolecki, J.Math.Anal.Appl. 126 (1987), 1-10.
- [14] I. Labuda, Compactoidness, Rocky Mountain J. Math. 36 (2006).
- [15] E. Michael, A note on closed maps and compact sets, Israel J. Math. 2 (1964), 173-176.
- [16] I. A. Vaı̆ns̆teı̆n, On closed mappings of metric spaces, Dokl.Akad.Nauk SSSR 57 (1947), 319- 321 (Russian).
- [17] 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, pp. 259-265, Dekker, New York 1976.
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Bibliografia
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bwmeta1.element.baztech-article-BUS2-0008-0058