query: Closure of topology sine $Y = \lbrace (x,\sin(\frac{1}{x})) : x > 0 \rbrace $
positive_passages.docid: 23414
positive_passages.text: Topologist's Sine Curve: A rigorous proof of why $\overline{S} = S \cup V$
negative_passages.docid: 91736
negative_passages.text: Explicit homeomorphism between open and closed rational intervals?
negative_passages.docid: 91682
negative_passages.text: Graph of a continuous function is closed
negative_passages.docid: 152105
negative_passages.text: When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?
negative_passages.docid: 158523
negative_passages.text: Topology: Proof that a finitely generated cone is closed
negative_passages.docid: 2575
negative_passages.text: Showing that $\mathbb{R}$ is connected
negative_passages.docid: 151329
negative_passages.text: Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
negative_passages.docid: 13804
negative_passages.text: Prove the set of which sin(nx) converges has Lebesgue measure zero (from Baby Rudin Chapter 11)
negative_passages.docid: 73690
negative_passages.text: If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
negative_passages.docid: 86860
negative_passages.text: Continuity of differentiable function $x^2\sin(1/x)$
negative_passages.docid: 83166
negative_passages.text: Homeomorphism(topological spaces) version of Cantor–Bernstein–Schroeder theorem
negative_passages.docid: 94244
negative_passages.text: $\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
negative_passages.docid: 39148
negative_passages.text: Does $\lim_{(x,y)\to(0,0)}[x\sin (1/y)+y\sin (1/x)]$ exist?
negative_passages.docid: 79213
negative_passages.text: Proof about a Topological space being arc connect
negative_passages.docid: 143586
negative_passages.text: Is $[0,1]$ a union of family of disjoint closed intervals?
negative_passages.docid: 94425
negative_passages.text: What is $\sup(\sin(n))$?
negative_passages.docid: 78471
negative_passages.text: Closure of $\{\frac{1}{n}\}:=M$