query: Prove that invertible metrices set is an open set in a given space, and the determinant is continuous
positive_passages.docid: 69542
positive_passages.text: Why do the $n \times n$ non-singular matrices form an "open" set?
negative_passages.docid: 64861
negative_passages.text: Intersection of open affines can be covered by open sets distinguished in *both*affines
negative_passages.docid: 49721
negative_passages.text: Prove the empty set is closed for a metric space (X,d).
negative_passages.docid: 135315
negative_passages.text: Proving whether a function on the set of real sequences is a metric
negative_passages.docid: 151046
negative_passages.text: Closure of the invertible operators on a Banach space
negative_passages.docid: 106398
negative_passages.text: If $A$ is invertible show that $\det(A) \neq 0$
negative_passages.docid: 94438
negative_passages.text: Show that the countable product of metric spaces is metrizable
negative_passages.docid: 2198
negative_passages.text: Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
negative_passages.docid: 31266
negative_passages.text: Proof of "the continuous image of a connected set is connected"
negative_passages.docid: 62118
negative_passages.text: Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function
negative_passages.docid: 124179
negative_passages.text: Proof that every metric space is normal
negative_passages.docid: 157753
negative_passages.text: Show that any set in a metric space can be written as the intersection of open sets
negative_passages.docid: 75215
negative_passages.text: Properties of invertible matrices
negative_passages.docid: 15365
negative_passages.text: Proving that the triangle inequality holds for a metric on $\mathbb{C}$
negative_passages.docid: 41611
negative_passages.text: Open and closed set in n by n matrices space.
negative_passages.docid: 46698
negative_passages.text: Showing a set is closed under inverses
negative_passages.docid: 140036
negative_passages.text: the determinant function is an open function?