query: If $ Y $ is irreducible set so is $cl(Y)$.
positive_passages.docid: 142093
positive_passages.text: The closure of an irreducible subset of an irreducible space is irreducible.
negative_passages.docid: 25471
negative_passages.text: Irreducibility of $x^n-x-1$ over $\mathbb Q$
negative_passages.docid: 24626
negative_passages.text: Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
negative_passages.docid: 5022
negative_passages.text: Can a set containing $0$ be purely imaginary?
negative_passages.docid: 144731
negative_passages.text: Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
negative_passages.docid: 116049
negative_passages.text: Every irreducible Polynomial is primitive or irreducible constant
negative_passages.docid: 93658
negative_passages.text: Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
negative_passages.docid: 103717
negative_passages.text: Topological Property of the Set of Integers
negative_passages.docid: 153934
negative_passages.text: How to prove that a set R\Z is open
negative_passages.docid: 51206
negative_passages.text: If $X$ and $Y$ are sets, their cartesian product $X\times Y$ is a set.
negative_passages.docid: 70049
negative_passages.text: Irreducible topological spaces and irreducible Hausdorff space
negative_passages.docid: 5293
negative_passages.text: Show that the logic $ \ \forall x \exists y \ P(x,y) \ $ is not logically equivalent to $ \ \exists x \forall y \ P(x,y) \ $
negative_passages.docid: 111935
negative_passages.text: Irreducible but not prime
negative_passages.docid: 84355
negative_passages.text: Methods to see if a polynomial is irreducible
negative_passages.docid: 28658
negative_passages.text: $R$ with an upper bound for degrees of irreducibles in $R[x]$
negative_passages.docid: 78549
negative_passages.text: Any prime is irreducible
negative_passages.docid: 114198
negative_passages.text: Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.