query: Are the connected components of $\mathbb{R}^n\setminus K$ in a finite number?
positive_passages.docid: 147197
positive_passages.text: Number of connected components of the complement of a compact
negative_passages.docid: 39746
negative_passages.text: How to prove that given set is a connected subset of the space of matrices?
negative_passages.docid: 723
negative_passages.text: Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
negative_passages.docid: 82474
negative_passages.text: Isometries of $\mathbb{R}^n$
negative_passages.docid: 151719
negative_passages.text: Connected set in $\mathbb{S}^1$
negative_passages.docid: 153107
negative_passages.text: Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?
negative_passages.docid: 12104
negative_passages.text: How to prove this result involving the quotient maps and connectedness?
negative_passages.docid: 106584
negative_passages.text: If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
negative_passages.docid: 55493
negative_passages.text: Showing that the path-connected component of the identity matrix in a subgroup of $GL_n(\Bbb R)$ is a normal subgroup
negative_passages.docid: 36044
negative_passages.text: Show $\Bbb R ^n$ with a finite set removed is still connected.
negative_passages.docid: 151928
negative_passages.text: How to prove that $N\setminus A$ is finite?
negative_passages.docid: 19754
negative_passages.text: $\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected?
negative_passages.docid: 123742
negative_passages.text: Proving connectedness of the $n$-sphere
negative_passages.docid: 11000
negative_passages.text: Fundamental group of $\mathbb{R}^2 \setminus (\mathbb{Z} \times \{0\})$
negative_passages.docid: 76381
negative_passages.text: Plain integer partitions of $n$ using $r$ parts
negative_passages.docid: 55070
negative_passages.text: Fundamental group of complement of $n$ lines through the origin in $\mathbb{R}^3$
negative_passages.docid: 88301
negative_passages.text: What are all of the connected subsets of $\mathbb{Q}$?