Geodesic
On free locally convex spaces
Filomat, Tome 36 (2022) no. 18, p. 6393

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DOI

Let L(X) be the free locally convex space over a Tychonoff space X. We prove that the following assertions are equivalent: (i) every functionally bounded subset of X is finite, (ii) L(X) is semi-reflexive, (iii) L(X) has the Grothendieck property, (iv) L(X) is semi-Montel. We characterize those spaces X, for which L(X) is c 0-quasibarrelled, distinguished or a (d f)-space. If X is a convergent sequence, then L(X) has the Glicksberg property, but the space L(X) endowed with its Mackey topology does not have the Schur property.
DOI : 10.2298/FIL2218393B
Classification : 46A03, 46A08, 54C35
Keywords: free locally convex space, b-feral, Grothendieck property, c0-quasibarrelled, (d f )-space 
Taras Banakh; Saak Gabriyelyan. On free locally convex spaces. Filomat, Tome 36 (2022) no. 18, p. 6393 . doi: 10.2298/FIL2218393B
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     author = {Taras Banakh and Saak Gabriyelyan},
     title = {On free locally convex spaces},
     journal = {Filomat},
     pages = {6393 },
     year = {2022},
     volume = {36},
     number = {18},
     doi = {10.2298/FIL2218393B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2218393B/}
}
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