# Tag Info

Accepted

### Does iterating the derivative infinitely many times give a smooth function whenever it converges?

I was able to adapt the accepted answer to this MathOverflow post to positively answer the question. The point is that one can squeeze more out of Petrov's Baire category argument if one applies it ...
• 91k

### Does the Brouwer fixed point theorem admit a constructive proof?

It's easier to think about the Intermediate Value Theorem, which is equivalent to the Brouwer Fixed-Point Theorem for the unit interval. The main issue is that dichotomy for (Cauchy) real numbers is ...
• 42.6k
Accepted

### Does the Brouwer fixed point theorem admit a constructive proof?

You are correct in observing the flaw in the claims for BFPT to be constructive: There is no algorithm that takes a sequence in the unit hypercube and outputs some accumulation point of it. This task ...
• 3,366

### Is the fixed point property for posets preserved by products?

This an open problem, as far as I know. The finite case was solved by Roddy in 1994. There were some more general results proved by other people later: see this paper by Bernd S. W. Schröder for a ...
• 827