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Background

I was reading Anthony Henderson’s paper “Bases For Certain Cohomology Representations Of The Symmetric Group “ (Ref.: arxiv.org/pdf/math/0508162) and came across the following statement in Proposition 2.6 on Page 9:

“V(1, n) can be identified with the subspace of V(r, n) spanned by [T] for T ∈ T (1, n)”.

While googling the internet trying to understand what is meant by the phrase “can be identified with,” I came across the following statement using the phrase “can be identified with”.

“W* [i.e., the dual space of W] can be identified with the subspace of V* [i.e., the dual space of V] consisting of all linear functionals that are zero.”

Here is a statement I created in which I believe I used the phrase “can be identified with” correctly:

“Vector space A, a subspace of vector space V, can be identified with vector space B, some other subspace of V.”

Here’s my question:

Does the phrase “can be identified with” mean the former subspace of V is a subset of and therefore a subspace of the latter subspace of V?

In other words, is the following statement equivalent to the statement above that I created?

“Vector space A, a subspace of vector space V, is also a subspace of vector space B, some other subspace of V.”

Thanks!

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# What is meant by can be identified with

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