A note on ANR%26apos;s

作者：Niemiec Piotr^*

来源：Topology and Its Applications, 2012, 159(1): 315-321.

DOI：10.1016/j.topol.2011.09.037

• Absolute neighborhood retract
• ANR
• Ball intersection property
• Urysohn universal space
• Complete metric space
• Almost contractive extensor

It is shown that if for a complete metric space (X, d) there is a constant epsilon %26gt; 0 such that the intersection boolean AND(n)(j=1) B(d)(x(j), r(j)) of open balls is nonempty for every finite system x(1), ..., x(n) is an element of X of centers and a corresponding system of radii r(1), ..., r(n) %26gt; 0 such that d(x(j), x(k)) %26lt;= epsilon and d(x(j), x(k)) %26lt; r(j)+ r(k) (j, k = 1, ..., n), then X is an ANR; and if in the above one may put epsilon = infinity, the space X is an AR. A certain criterion for an incomplete metric space to be an A(N)R is presented.

• 出版日期2012-1-1