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Update properties/P000238.md
Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com>
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$X$ is homeomorphic to a topological vector space (TVS) over $\mathbb R$.
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Equivalently, there exists a continuous commutative group operation $(x, y) \mapsto x + y$, and a continuous scalar multiplication operation $\mathbb{R} \times X \to X$, $(\lambda, x) \mapsto \lambda x$, where $\mathbb{R}$ has the Euclidean topology, such that these operations together satisfy the axioms of a real vector space.
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Equivalently, there exists a continuous commutative group operation $(x, y) \mapsto x + y$ on $X$, and a continuous scalar multiplication operation $\mathbb{R} \times X \to X$, $(\lambda, x) \mapsto \lambda x$, where $\mathbb{R}$ has the Euclidean topology, such that these operations together satisfy the axioms of a real vector space.
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Many authors, such as Rudin, additionally require separation axioms like {P3}, {P2} or {P1}, though we do not.
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