First reference I've seen for someone suggesting using half size 3 x 5" index cards so that they could use commercially available Magic: The Gathering (MTG) boxes.

Oxford and possibly other manufacturers already make 1/2 size 3 x 5" index cards.

I just discovered that the subspaces in vector spaces are very different compare to metric spaces.

1. A subspace of a metric space just have to be a metric space.
2. A subspace of a vector space will still have to retain the vector space structure. But if it's viewed as a metric space, this doesn't have to be the case.

Also take note that this is talking about any spaces of dimensions.

Continuous mapping preserves compactness in finite dimensional spaces.

Compact Closed unit ball in a normed spaces would mean that we have finite dimension.

Riesz's Lemma, preparing for a theorem about the norm ball in finite dimensional spaces.

2.5 Push through to completion.