query: Is the set $\{\big(x,\sin(1/x)\big):x\ne 0 \}$ connected in usual metric of $\mathbb R^2$?
positive_passages.docid: 27581
positive_passages.text: Topologist's sine curve is connected
negative_passages.docid: 50645
negative_passages.text: Is the following set (path) connected?
negative_passages.docid: 2575
negative_passages.text: Showing that $\mathbb{R}$ is connected
negative_passages.docid: 156520
negative_passages.text: Intervals are connected and the only connected sets in $\mathbb{R}$
negative_passages.docid: 30079
negative_passages.text: Is for open connected $U$ the set $U_\varepsilon$ for small $\varepsilon$ connected?
negative_passages.docid: 59424
negative_passages.text: Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
negative_passages.docid: 22865
negative_passages.text: Sine function dense in $[-1,1]$
negative_passages.docid: 52014
negative_passages.text: Showing $(C[0,1], d_1)$ is not a complete metric space
negative_passages.docid: 147287
negative_passages.text: Is it possible to construct a metric in $\mathbb{R}^n $ s.t. it does not induce CONVEX balls?
negative_passages.docid: 35069
negative_passages.text: Connectedness of the boundary
negative_passages.docid: 84791
negative_passages.text: Is every connected metric space with at least two points uncountable?
negative_passages.docid: 96458
negative_passages.text: Does $X_n \overset{L^2}{\rightarrow} X$ imply $X_n^2 \overset{L^1}{\rightarrow} X^2$?
negative_passages.docid: 156479
negative_passages.text: Fractal dimension of set in $\mathbb{R}^2$
negative_passages.docid: 51514
negative_passages.text: Is $n \sin n$ dense on the real line?
negative_passages.docid: 21599
negative_passages.text: $(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
negative_passages.docid: 114047
negative_passages.text: Metric $d(x,y)=\frac{|x-y|}{\sqrt{1+x^2}\sqrt{1+y^2}}$ on $\mathbb{R}$
negative_passages.docid: 36631
negative_passages.text: Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?