a question about compact set, how to prove there exists f(y)=y
14509
Contraction Map on Compact Normed Space has a Fixed Point
61500
If f is continous and exist real numbers show that $f(x)=0$
35889
Suppose that f(0) = f(1) = 0 and x ∈ (0, 1). Prove that there exists c ∈ (0, 1) such that f'(c) = f(x).
15354
Formal proof of $\exists x \forall y P(x,y) \implies \forall y \exists x P(x,y)$
73154
Compact subset in colimit of spaces
66948
Proving question on sets
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
110744
How to prove that a compact set in a Hausdorff topological space is closed?
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
37183
Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
97772
An example of a function which satisfies $\sup_{y}\inf_{x}f(x,y)<\inf_{x}\sup_{y}f(x,y)$
16826
prove that every infinite subset of compact set H has a limit point (Explanation)
27800
For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
107772
Separability of functions with compact support
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space