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theorems/T000881.md
@@ -11,7 +11,7 @@ refs:
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name: Answer to "Cardinality of a vector space versus the cardinality of its basis"
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---
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-The vector space $V$ of finite formal linear combinations of elements from $X$ over $\mathbb{R}$ has the
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-same cardinality as $X$; see {{mathse:541116}}. Hence there exists a bijection
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-$X \to V$. With the indiscrete topology $V$ is a real TVS,
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-and this bijection is a homeomorphism
+Suppose $|X|=\kappa\ge\mathfrak c$.
+Let $V$ be a vector space over $\mathbb R$ of (algebraic) dimension $\kappa$.
+As shown in {{mathse:541116}}, $V$ also has cardinality $\kappa$.
+With the indiscrete topology $V$ is a real TVS and is homeomorphic to $X$ via any bijection between the two.
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