Geodesic
Center Points Of Nets
Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 418-422

Voir la notice de l'article provenant de la source Cambridge University Press

Suppose x = (x∝) is a net with values in a metric space X having metric ρ. If a point z in X can be found to minimize then z is called a center point (c.p.) of x. The space X is (netwise) c.p. complete if every bounded net has at least one c.p.; it is sequentially c.p. complete if every bounded sequence has a c.p. Netwise c.p. completeness implies sequential c.p. completeness, and the latter implies completeness since any c.p. of a Cauchy sequence will necessarily be a limit point of that sequence.These notions are related to the set centers of Calder et al. [2]. 
Anderson, C. L.; Hyams, W. H.; McKnight, C. K. Center Points Of Nets. Canadian journal of mathematics, Tome 27 (1975) no. 2, pp. 418-422. doi: 10.4153/CJM-1975-049-8
@article{10_4153_CJM_1975_049_8,
     author = {Anderson, C. L. and Hyams, W. H. and McKnight, C. K.},
     title = {Center {Points} {Of} {Nets}},
     journal = {Canadian journal of mathematics},
     pages = {418--422},
     year = {1975},
     volume = {27},
     number = {2},
     doi = {10.4153/CJM-1975-049-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-049-8/}
}
TY  - JOUR
AU  - Anderson, C. L.
AU  - Hyams, W. H.
AU  - McKnight, C. K.
TI  - Center Points Of Nets
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 418
EP  - 422
VL  - 27
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-049-8/
DO  - 10.4153/CJM-1975-049-8
ID  - 10_4153_CJM_1975_049_8
ER  - 
%0 Journal Article
%A Anderson, C. L.
%A Hyams, W. H.
%A McKnight, C. K.
%T Center Points Of Nets
%J Canadian journal of mathematics
%D 1975
%P 418-422
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-049-8/
%R 10.4153/CJM-1975-049-8
%F 10_4153_CJM_1975_049_8

[1] 1. Anderson, C. L., Hyams, W. H., and McKnight, C. K., Generalization of a fixed point theorem of M. Edelstein (to appear). Google Scholar

[2] 2. Calder, J. R., Coleman, W. P., and Harris, R. L., Centers of infinite bounded sets in a normed space, Can. J. Math. 25 (1973), 986–999. Google Scholar

[3] 3. Edelstein, M., The construction of an asymptotic center with a fixed point property, Bull. Amer. Math. Soc. 78 (1972), 206–208. Google Scholar

[4] 4. Garkavi, A. L., The best possible net and best possible cross-section of a set in a normed space, Amer. Math. Soc. Transi. Ser. 2, 39 (1964), 111–132. Google Scholar

[5] 5. Hyams, W. H., Sequentially center point complete spaces, Ph.D. Thesis, University of Southwestern Louisiana, 1973. Google Scholar

[6] 6. Mizel, V. and Sundaresun, K., Banach sequence spaces, Arch. Math. (Basel) 19 (1968), 59–69. Google Scholar

[7] 7. Ruckle, W., On perfect symmetric BK spaces, Math. Ann. 175 (1968), 121–126. Google Scholar

Cité par Sources :