Is the set of matrices with rank at most $r$ closed?
127591
How to prove that the collection of rank-k matrices forms a closed subset of the space of matrices?
10180
How to prove that this set is closed?
82688
Least rank of a matrix
39353
Matrices that can only be permutation matrices
94639
Proof that the rank of a skew-symmetric matrix is at least $2$
15417
Tricky problem on skew-symmetric matrices
78117
Closed property of nonempty finite set
113169
Number of $\pm 1$ matrices whose determinant is negative or zero
97487
How to prove whether a matrix has rank $1$
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
34043
A rank-one matrix is the product of two vectors
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
115272
Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed
64517
Prove that row rank of a matrix equals column rank
21758
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
119435
Rank of the difference of matrices
158569
Proving a particular subset of $R^n$ is closed