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1993 | 142 | 2 | 101-122
Tytuł artykułu

On linear operators and functors extending pseudometrics

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For some pairs (X,A), where X is a metrizable topological space and A its closed subset, continuous, linear (i.e., additive and positive-homogeneous) operators extending metrics for A to metrics for X are constructed. They are defined by explicit analytic formulas, and also regarded as functors between certain categories. An essential role is played by "squeezed cones" related to the classical cone construction. The main result: if A is a nondegenerate absolute neighborhood retract for metric spaces, then continuous linear operators extending metrics always exist.
Słowa kluczowe
Rocznik
Tom
142
Numer
2
Strony
101-122
Opis fizyczny
Daty
wydano
1993
otrzymano
1991-03-25
poprawiono
1991-12-12
poprawiono
1992-05-12
poprawiono
1992-08-10
Twórcy
autor
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
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  • [AM] D. Avis and Mutt, All the facets of the six-point Hamming cone, European J. Combin. 10 (1989), 309-312.
  • [B] C. Bessaga, Functional analytic aspects of geometry. Linear extending of metrics and related problems, in: Progress in Functional Analysis, Proceedings of the Peniscola Meeting 1990 on the occasion of the 60th birthday of Professor M. Valdivia, North-Holland Math. Stud. 170, North-Holland, Amsterdam 1992, 247-257.
  • [BP] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa 1975.
  • [Bo] K. Borsuk, Über Isomorphie der Funktionalräume, Bull. Internat. Acad. Polon. Sér. A 1933, 1-10.
  • [Bor] K. Borsuk, Theory of Retracts, PWN, Warszawa 1967.
  • [] K. Borsuk, Theory of Shape, PWN, Warszawa 1975.
  • [D] M. Deza (Tylkin), On Hamming geometry of unitary cubes, Dokl. Akad. Nauk SSSR 134 (1960), 1037-1040 (in Russian).
  • [De] M. Deza (Tylkin), Matrices des formes quadratiques non négatives pour des arguments binaires, C. R. Acad. Sci. Paris Sér. A-B 277 (1973), A873-A875.
  • [Du] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367.
  • [H] F. Hausdorff, Erweiterung einer Homöomorphie, Fund. Math. 16 (1930), 353-360.
  • [K] J. B. Kelly, Metric inequalities and symmetric differences, in: Inequalities II, Academic Press, New York 1970, 193-212.
  • [Ke] J. B. Kelly, Hypermetric spaces, in: The Geometry of Metric and Linear Spaces, Lecture Notes in Math. 490, Springer, 1975, 17-31.
  • [L] J. Luukkainen, Extension of spaces, maps, and metrics in Lipschitz topology, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 17 (1978), 1-62.
  • [N] Nguyen To Nhu, Extending metrics uniformly, Colloq. Math. 43 (1980), 91-97.
  • [KN] Nguyen Van Khue and Nguyen To Nhu, Two extensors of metrics, Bull. Acad. Polon. Sci. 29 (1981), 285-291.
  • [T] H. Toruńczyk, A short proof of Hausdorff's theorem on extending metrics, Fund. Math. 77 (1972), 191-193.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv142i2p101bwm
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