域上向量空间子空间的可拓算子 \(\mathbb{F}_2\)

Pub Date : 2022-10-10 DOI:10.1134/S001626632202006X
O. V. Sipacheva, A. A. Solonkov
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引用次数: 0

摘要

证明了由可分层空间\(X\)生成的域\(\mathbb{F}_2=\{0,1\}\)上的自由拓扑向量空间\(B(X)\)是可分层的,因此,对于任何闭子空间\(F\subset B(X)\)(特别是\(F=X\))和任何局部凸空间\(E\),连续映射空间之间存在一个线性扩展算子\(C(F,E)\to C(B(X),E)\)。
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Extension Operator for Subspaces of Vector Spaces over the Field \(\mathbb{F}_2\)

In is proved that the free topological vector space \(B(X)\) over the field \(\mathbb{F}_2=\{0,1\}\) generated by a stratifiable space \(X\) is stratifiable, and therefore, for any closed subspace \(F\subset B(X)\) (in particular, for \(F=X\)) and any locally convex space \(E\), there exists a linear extension operator \(C(F,E)\to C(B(X),E)\) between spaces of continuous maps.

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