Answer by K. Carrillo for Extension of linearly independent set to a basis in...
Let be $V$ a vector space and $W\leq V$ a subspace of $V$ with basis $Y$. If we consider the quotient space $V/W$ , by Zorn's lemma, we can obtain a basis of $V/W$, denoted $\overline{S}$.If $v\in V$,...
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Let $V$ be a vector space, $S\subseteq V$ a linearly independent subset and $\mathcal{A}=\{T\subseteq V: S\subseteq T \text{and $T$ is linearly independent}\}$. It is easy to see that any chain on...
View ArticleExtension of linearly independent set to a basis in an infinite dimensional...
Is it always possible to extend a linearly independent set to a basis in infinite dimensional vector space?I was proving with the following argument:If S is a linearly independent set, if it spans the...
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