query: Connectedness of an irreducible algebraic curve without singularities.
positive_passages.docid: 28079
positive_passages.text: Do these definitions of irreducibility of algebraic sets coincide?
negative_passages.docid: 16593
negative_passages.text: Irreducible Spectrum implies Zero-Divisors are Nilpotent
negative_passages.docid: 52528
negative_passages.text: Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
negative_passages.docid: 53012
negative_passages.text: Irreducibility of a polynomial if it has no root (Capelli)
negative_passages.docid: 60816
negative_passages.text: Irreducibility of special cyclotomic polynomial.
negative_passages.docid: 101712
negative_passages.text: Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
negative_passages.docid: 70249
negative_passages.text: Irreducibility of Polynomials in $k[x,y]$
negative_passages.docid: 61429
negative_passages.text: Is the algebraic closure of a $p$-adic field complete
negative_passages.docid: 123742
negative_passages.text: Proving connectedness of the $n$-sphere
negative_passages.docid: 1060
negative_passages.text: Minimal polynomial of intermediate extensions under Galois extensions.
negative_passages.docid: 27253
negative_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: 68926
negative_passages.text: Finitely generated singular homology
negative_passages.docid: 93111
negative_passages.text: Finiteness of the Algebraic Closure
negative_passages.docid: 42412
negative_passages.text: Singular homology $S^{n}$ with rational coefficients
negative_passages.docid: 100437
negative_passages.text: Classification of connected subsets of the real line (up to homeomorphism)
negative_passages.docid: 15865
negative_passages.text: Show that $X = \{ (x,y) \in\mathbb{R}^2\mid x \in \mathbb{Q}\text{ or }y \in \mathbb{Q}\}$ is path connected.
negative_passages.docid: 122050
negative_passages.text: Algebraic extension of perfect field in which every polynomial has a root is algebraically closed