SUBSPACES OF THE FREE TOPOLOGICAL VECTOR SPACE ON THE UNIT INTERVAL
2017 ◽
Vol 97
(1)
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pp. 110-118
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Keyword(s):
For a Tychonoff space $X$, let $\mathbb{V}(X)$ be the free topological vector space over $X$, $A(X)$ the free abelian topological group over $X$ and $\mathbb{I}$ the unit interval with its usual topology. It is proved here that if $X$ is a subspace of $\mathbb{I}$, then the following are equivalent: $\mathbb{V}(X)$ can be embedded in $\mathbb{V}(\mathbb{I})$ as a topological vector subspace; $A(X)$ can be embedded in $A(\mathbb{I})$ as a topological subgroup; $X$ is locally compact.
2003 ◽
Vol 68
(2)
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pp. 243-265
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1982 ◽
Vol 14
(5)
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pp. 399-402
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1997 ◽
Vol 56
(3)
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pp. 529-538
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1974 ◽
Vol 26
(4)
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pp. 841-853
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2008 ◽
Vol 78
(3)
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pp. 487-495
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1993 ◽
Vol 114
(3)
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pp. 439-442
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2019 ◽
Vol 101
(2)
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pp. 311-324
1986 ◽
Vol 100
(2)
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pp. 347-353
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