On Convex Sets with Convex-Hereditary CEP

• Autorzy: Dobrowolski T.

Identyfikatory

DOI

10.4064/ba59-3-4

• Języki publikacji: EN

Abstrakty

EN

CEP stands for the compact extension property. We characterize nonlocally convex complete metric linear spaces with convex-hereditary CEP.

Słowa kluczowe

EN

nonlocally convex space; convex set; Klee-admissible; compact extension property; metric limits

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2011
• Tom: Vol. 59, no 3
• Strony: 215--222
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Dobrowolski T.

• Department of Mathematics Pittsburg State University Pittsburg, KS 66762, U.S.A.
• Faculty of Mathematics and Natural Sciences College of Sciences Cardinal Stefan Wyszyński University Wóycickiego 1/3 01-938 Warszawa, Poland

Bibliografia

• [BD] C. Bessaga and T. Dobrowolski, Affine and homeomorphic embeddings into `2, Proc. Amer. Math. Soc. 125 (1997), 259–268.
• [BP] C. Bessaga and A. Pełczynski, Selected Topics in Infinite-Dimensional Topology, PWN – Polish Sci. Publ., Warszawa, 1975.
• [vBvM] J. van der Bijl and J. van Mill, Linear spaces, absolute retracts, and the compact extension property, Proc. Amer. Math. Soc. 104 (1988), 942–952.
• [Ca1] R. Cauty, Un espace métrique linéaire qui n’est pas un rétracte absolu, Fund. Math. 146 (1994), 85–99.
• [Ca2] —, Solution du problème de point fixe de Schauder, ibid. 170 (2001), 231–246.
• [Ca3] —, Rétractes absolus de voisinage algébriques, Serdica Math. J. 31 (2005), 309–354.
• [Do] T. Dobrowolski, On extending mappings into nonlocally convex linear metric spaces, Proc. Amer. Math. Soc. Math. 93 (1985), 555–560.
• [DK] T. Dobrowolski and N. J. Kalton, Cauty’s space enhanced, Topology Appl., to appear.
• [DvM] T. Dobrowolski and J. van Mill, Selections and near-selections in metric linear spaces without local convexity, Fund. Math. 192 (2006), 215–232.
• [DS] T. Dobrowolski and S. Spiez, Fixed-point property “proofs” relying on Cauty’s resolution mapping contain a gap, submitted.
• [DT] T. Dobrowolski and H. Torunczyk, On metric linear spaces homeomorphic to l2 and compact convex sets homeomorphic to Q, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 883–887.
• [KPR] N. J. Kalton, N. T. Peck, and J. W. Roberts, An F-space Sampler, London Math. Soc. Lecture Note Ser. 89, Cambridge Univ. Press, Cambridge, 1984.
• [K1] V. Klee, Leray–Schauder theory without local convexity, Math. Ann. 141 (1960), 286–296; Corrections, ibid. 145 (1962), 464–465.
• [K2] —, Shrinkable neighborhoods in Hausdorff linear spaces, ibid. 141 (1960), 281–285.
• [Ku] K. Kuratowski, Topology, Vol. I, Academic Press, New York, and PWN, Warszawa, 1966.
• [TT] L. H. Tri and N. H. Thanh, Some remarks on the AR-problem, preprint.