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The first acquaintance of every student with dimension theory is in linear algebra, when the dimension of a vector space V is introduced as the cardinal number of a basis. This definition is based on two results: bases exist and any two of them are equipotent. But the essential ideas of the respective proofs are easily veiled behind algebraic calculations. They become much clearer if one works in greater generality where only the facts which are essential for obtaining the results can be used.
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