query: Showing $f: S^1 \rightarrow S^1$ has certainly $k-2$ other fixed points, besides $x_0$
positive_passages.docid: 23239
positive_passages.text: Prove that the following map has at least $k-2$ fixed points
negative_passages.docid: 54222
negative_passages.text: Prove the map has a fixed point
negative_passages.docid: 57639
negative_passages.text: Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
negative_passages.docid: 33370
negative_passages.text: Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff
negative_passages.docid: 107076
negative_passages.text: Prove $S^1$ is not homeomorphic to $S^2$ using connectedness
negative_passages.docid: 83985
negative_passages.text: Equivalent statements to fixed-point theorem
negative_passages.docid: 14975
negative_passages.text: Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
negative_passages.docid: 26478
negative_passages.text: Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
negative_passages.docid: 100740
negative_passages.text: proof of that a continuous function has a fixed point
negative_passages.docid: 72642
negative_passages.text: Continuous bijection from $(a,b) \to S^1$?
negative_passages.docid: 28781
negative_passages.text: $k^{2}+(k+1)^{2}$ being a perfect square for infinitely many $k$
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 72889
negative_passages.text: Existence of fixed point given a mapping
negative_passages.docid: 17859
negative_passages.text: Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
negative_passages.docid: 8039
negative_passages.text: an analytic function from unit disk to unit disk with two fixed point
negative_passages.docid: 8799
negative_passages.text: Mapping homotopic to the identity map has a fixed point
negative_passages.docid: 61884
negative_passages.text: If $T^n$ is $q$-contractive, $T$ exactly has one fixed point