Note that in a case of infinite dimensionality like this, the range can be the whole Banach space even though the domain is only a proper subspace thereof.
2.
A complex reflection group " W " is "'irreducible "'if the only " W "-invariant proper subspace of the corresponding vector space is the origin.
3.
*PM : every finite dimensional proper subspace of a normed space is nowhere dense, id = 6687-- WP guess : every finite dimensional proper subspace of a normed space is nowhere dense-- Status:
4.
*PM : every finite dimensional proper subspace of a normed space is nowhere dense, id = 6687-- WP guess : every finite dimensional proper subspace of a normed space is nowhere dense-- Status:
5.
A Toronto space is a topological space that is homeomorphic to every proper subspace of the same cardinality ( it may be a good exercise to check that the topological space you mention is indeed a Toronto space ).
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