Geodesic
Extension Operator for Subspaces of Vector Spaces over the Field $\mathbb{F}_2$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 64-74

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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, Dugundji–Borges theorem, topological vector space over $\mathbb{F}_2$, free Boolean topological group.
Mots-clés : stratifiable space 
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     author = {O. V. Sipacheva and A. A. Solonkov},
     title = {Extension {Operator} for {Subspaces} of {Vector} {Spaces} over the {Field} $\mathbb{F}_2$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {64--74},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a5/}
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O. V. Sipacheva; A. A. Solonkov. Extension Operator for Subspaces of Vector Spaces over the Field $\mathbb{F}_2$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 64-74. http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a5/