Proof of `The Grassmannian of k-dimensional subspaces is Polish` (1st statement)
groundedproofs/Lax606786Proofs/Grassmannian.lean · lax-606786
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
A Cauchy sequence of unit spheres converges in the space of compact sets; Riesz's lemma shows that the limit still spans a -dimensional space, and a frame chosen in the limit transports to the sequence.