query: Path connectedness of a subset of $\mathbb{R}^2$
positive_passages.docid: 27253
positive_passages.text: Path connectedness of the set $\{(x,y):(x+1)^{2}+y^{2}\leq 1\}\cup\{(x,y):y=x\sin(\frac{1}{x}),x>0\}$
negative_passages.docid: 27661
negative_passages.text: The closed graph theorem in topology
negative_passages.docid: 151719
negative_passages.text: Connected set in $\mathbb{S}^1$
negative_passages.docid: 75829
negative_passages.text: Dimension of open subsets of $R^n$
negative_passages.docid: 33822
negative_passages.text: Is there a monoid structure on the set of paths of a graph?
negative_passages.docid: 102084
negative_passages.text: How to show path-connectedness of $GL(n,\mathbb{C})$
negative_passages.docid: 4602
negative_passages.text: Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
negative_passages.docid: 100437
negative_passages.text: Classification of connected subsets of the real line (up to homeomorphism)
negative_passages.docid: 19754
negative_passages.text: $\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
negative_passages.docid: 93986
negative_passages.text: Connectivity, Path Connectivity and Differentiability
negative_passages.docid: 26919
negative_passages.text: Intersection of Connected Sets
negative_passages.docid: 2575
negative_passages.text: Showing that $\mathbb{R}$ is connected
negative_passages.docid: 47730
negative_passages.text: graph is dense in $\mathbb{R}^2$
negative_passages.docid: 144383
negative_passages.text: The closure of a connected set in a topological space is connected
negative_passages.docid: 156520
negative_passages.text: Intervals are connected and the only connected sets in $\mathbb{R}$
negative_passages.docid: 136158
negative_passages.text: $X$ has Indiscrete topology $\implies$ any subset of $X$ is connected
negative_passages.docid: 42811
negative_passages.text: Product of path connected spaces is path connected