query: Prove $T: X \to X$ has a fixed point if there exists an $x \in X$, so that $T(x) = x$
positive_passages.docid: 30455
positive_passages.text: Show that any continuous $f:[0,1] \rightarrow [0,1]$ has a fixed point $\zeta$
negative_passages.docid: 149801
negative_passages.text: prove that $TS = ST$
negative_passages.docid: 52095
negative_passages.text: Prove either $G=ST$ or |$G|\geq|S|+|T|$
negative_passages.docid: 76694
negative_passages.text: Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
negative_passages.docid: 59717
negative_passages.text: Generalization of Banach's fixed point theorem
negative_passages.docid: 72889
negative_passages.text: Existence of fixed point given a mapping
negative_passages.docid: 48592
negative_passages.text: Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
negative_passages.docid: 122663
negative_passages.text: Proving $T$ and $U$ are equal if I know $(X,T)$ and $(X,U)$ are hausdorff and compact
negative_passages.docid: 113083
negative_passages.text: How to prove a set equality?
negative_passages.docid: 59724
negative_passages.text: Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
negative_passages.docid: 99906
negative_passages.text: If $f'(c)$ exists then $\lim_{x\to c} f(x)=f(c)$
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 37331
negative_passages.text: Prove that every set with more than one element has a permutation without fixed points
negative_passages.docid: 156850
negative_passages.text: Fix-Point Theorem Proof.
negative_passages.docid: 61884
negative_passages.text: If $T^n$ is $q$-contractive, $T$ exactly has one fixed point
negative_passages.docid: 72044
negative_passages.text: prove $x \mapsto x^2$ is continuous
negative_passages.docid: 58664
negative_passages.text: Proving a function is continuous for a fixed variable