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## Main Question or Discussion Point

What does it mean for a condition to be "open"? E.g. it is said that det(A)≠0 is an open condition for a matrix group.

Furthermore, this implies that GL(n) has the same dimensions as the group of all nxn matrices as, and I quote, "the subgroup of matrices with det(A)=0 is a subset of measure zero".

1. Could you explain why this is true?

2. Could you shed light on what kind of measure we are talking about here (Lebesgue, Dirac, or else)?

Thank you.

Furthermore, this implies that GL(n) has the same dimensions as the group of all nxn matrices as, and I quote, "the subgroup of matrices with det(A)=0 is a subset of measure zero".

1. Could you explain why this is true?

2. Could you shed light on what kind of measure we are talking about here (Lebesgue, Dirac, or else)?

Thank you.