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We prove several dichotomies on linear embeddings between Banach spaces.Given an arbitrary Banach space X with a basis, we show that the relations ofisomorphism and bi-embedding are meager or co-meager on the Polish set ofblock-subspaces of X. We relate this result with tightness and minimality ofBanach spaces. Examples and open questions are provided.

Tightness of Banach spaces and Baire category