Extension Operator for Subspaces of Vector Spaces over the Field $\mathbb{F}_2$

O. V. Sipacheva, A. A. Solonkov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Keywords: extension operator, stratifiable space, Dugundji–Borges theorem, topological vector space over $\mathbb{F}_2$, free Boolean topological group.

UDC: 515.12

MSC: 46A99

Received: 29.10.2021
Revised: 29.10.2021
Accepted: 22.11.2021

DOI: 10.4213/faa3959

 English version: Functional Analysis and Its Applications, 2022, 56:2, 130–137

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