Metrization of Symmetric Spaces
Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 986-990
Voir la notice de l'article provenant de la source Cambridge University Press
A distance function d on a set X is a function X × X → [0, ∞ ) satisfying (1) d(x, y) = 0 if and only if x = y, and (2) d(x, y) = d(y, x). Such a function determines a topology T on X by agreeing that U is an open set if it contains an ∈-sphere N(p; ∈)( = {x: d(p, x) < ∈}} about each of its points. Equivalently, F is closed if and only if d(x, F) > 0 for each x ∈ X — F. A topological space is symmetrizable via a distance function d if its topology is determined by d as above, and semi-metrizahle via d if x ∈ Ā is equivalent to d(x, A) = 0.
III, P. W. Harley; Faulkner, G. D. Metrization of Symmetric Spaces. Canadian journal of mathematics, Tome 27 (1975) no. 5, pp. 986-990. doi: 10.4153/CJM-1975-102-x
@article{10_4153_CJM_1975_102_x,
author = {III, P. W. Harley and Faulkner, G. D.},
title = {Metrization of {Symmetric} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {986--990},
year = {1975},
volume = {27},
number = {5},
doi = {10.4153/CJM-1975-102-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-102-x/}
}
[1] 1. Arhangelskii, A. V., Mappings and spaces, Russian Math. Surveys 21 (1966), 115–162. Google Scholar
[2] 2. Hodel, R. E., Some results in metrization theory, 1950–1972, V.P.I. Conference, April, 1973. Google Scholar
[3] 3. Jones, F. B., Metrization, Amer. Math. Soc. Monthly 73 (1966), 571–576. Google Scholar
[4] 4. Martin, H. Y., Metrization of symmetric spaces and regular maps, Proc. Amer. Math. Soc. 35 (1972), 269–274. Google Scholar
Cité par Sources :