# On linear operators and functors extending pseudometrics

Fundamenta Mathematicae (1993)

- Volume: 142, Issue: 2, page 101-122
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topBessaga, C.. "On linear operators and functors extending pseudometrics." Fundamenta Mathematicae 142.2 (1993): 101-122. <http://eudml.org/doc/211975>.

@article{Bessaga1993,

abstract = {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.},

author = {Bessaga, C.},

journal = {Fundamenta Mathematicae},

keywords = {squeezed cones; metrizable topological space},

language = {eng},

number = {2},

pages = {101-122},

title = {On linear operators and functors extending pseudometrics},

url = {http://eudml.org/doc/211975},

volume = {142},

year = {1993},

}

TY - JOUR

AU - Bessaga, C.

TI - On linear operators and functors extending pseudometrics

JO - Fundamenta Mathematicae

PY - 1993

VL - 142

IS - 2

SP - 101

EP - 122

AB - 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.

LA - eng

KW - squeezed cones; metrizable topological space

UR - http://eudml.org/doc/211975

ER -

## References

top- [AS] R. D. Anderson and R. Schori, Factors of infinite-dimensional manifolds, Trans. Amer. Math. Soc. 142 (1969), 315-330. Zbl0187.20505
- [AD] P. Assouad and M. Deza, Metric subspaces of ${L}^{1}$, Publ. Math. Orsay 3 (1982), 47 pp. Zbl0478.05021
- [Av] D. Avis, Hypermetric spaces and the Hamming cone, Canad. J. Math. 33 (1981), 795-802. Zbl0445.52008
- [AM] D. Avis and Mutt, All the facets of the six-point Hamming cone, European J. Combin. 10 (1989), 309-312. Zbl0686.52001
- [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. Zbl0771.54027
- [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. Zbl0007.25201
- [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. Zbl0275.05014
- [Du] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367. Zbl0043.38105
- [H] F. Hausdorff, Erweiterung einer Homöomorphie, Fund. Math. 16 (1930), 353-360. Zbl56.0508.03
- [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. Zbl0396.54025
- [N] Nguyen To Nhu, Extending metrics uniformly, Colloq. Math. 43 (1980), 91-97. Zbl0459.54019
- [KN] Nguyen Van Khue and Nguyen To Nhu, Two extensors of metrics, Bull. Acad. Polon. Sci. 29 (1981), 285-291. Zbl0466.54026
- [T] H. Toruńczyk, A short proof of Hausdorff's theorem on extending metrics, Fund. Math. 77 (1972), 191-193. Zbl0248.54035

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.