Geodesic
Subtle hyperplanes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1553-1555.

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We show that the countably-dimensional vector space $C_{00}$ of all sequences with finite support contains a convex cone $K$ that does not include straight lines and is closed Archiemedean but not closed in the Mackey topology $\tau$ corresponding to the duality $\langle C_{00}| F\rangle$, where $F$ is a hyperplane in the algebraic dual space $C_{00}^\#$.
Keywords: cone, duality of topology vector spaces. 
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     author = {K. V. Storozhuk},
     title = {Subtle hyperplanes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1553--1555},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a141/}
}
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K. V. Storozhuk. Subtle hyperplanes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1553-1555. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a141/

[1] Gutman A. E., Emel'yanov E. Yu., Matyukhin A. V., “Nonclosed Archimedean cones in locally convex spaces”, Vladikavkaz. Mat. Zh., 17:3 (2015), 36–43 (in Russian) | MR