Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $W$ be a real Hilbert space of dimension $n$ and $V$ a Hilbert subspace of dimension $m$. Assume that $f_1,\cdots,f_k$ are points in $W$ such that the following holds:

  1. there exists $\sigma>0$ such that $dist(f_i,V)\geq\sigma$ for $i=1,2,\cdots,k$,
  2. there exists $0<\delta\leq\sigma$ such that the balls $B(f_i,\delta)$ are disjoint for $i=1,2,\cdots,k$,
  3. there exists $L>0$ such that $||f_i||_2\leq L$ for $i=1,2,\cdots,k$.

Can you find a good bound on $k$ (the number of the points $f_i$) involving $n,m,\sigma,\delta,L$?

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.