On linear topological spaces (linearly) homeomorphic to $\Bbb R^\infty$

Author
T. Banakh
Department of Mathematics, Lviv University, Universytetska 1, Lviv,290602, Ukraine
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 $\Bbb R^\infty=\varinjlim \Bbb R^n$.
Keywords
infinite-dimensional locally convex topological space, direct limit
DOI
doi:10.30970/ms.9.1.99-101
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
Volume
9
Issue
1
Year
1998
Journal
Matematychni Studii
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