On linear topological spaces (linearly) homeomorphic to $\Bbb R^\infty$ |
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| Author |
Department of Mathematics, Lviv University, Universytetska 1, Lviv,290602, Ukraine
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| Abstract |
We prove that every infinite-dimensional (locally convex) linear topological
space that can be expressed as a direct limit of finite-dimensional
metrizable compacta is (linearly) homeomorphic to the space
$\Bbb R^\infty=\varinjlim \Bbb R^n$.
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| Keywords |
infinite-dimensional locally convex topological space, direct limit
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| DOI |
doi:10.30970/ms.9.1.99-101
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Reference |
1. D.W. Curtis, T. Dobrowolski, J. Mogilski Some applications of the topological characterizations of the sigma-compact spaces $l_f^2$ and $\Sigma$// Trans. Amer. Math. Soc.-- 1984 V.284 p.837--846
2. Sa. K. Sakai On $\Bbb R^\infty$-manifolds and $Q^\infty$-manifolds // Top. Appl.-- 1984 V.18 p.69--79 |
| Pages |
99-101
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| Volume |
9
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| Issue |
1
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| Year |
1998
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| Journal |
Matematychni Studii
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