Geodesic
An Internal Solution to the Problem of Linearization of a Convexity Space
Canadian mathematical bulletin, Tome 19 (1976) no. 4, pp. 487-494

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Following Kay and Womble [2] an abstract convexity structure on a set X is a collection ξ of subsets of X which includes the empty set, X and is closed under arbitrary intersections. One of the natural problems that arises in convexity structures is to give necessary and sufficient conditions for the existance of a linear structure on X such that the collection of all convex sets in the resulting linear space is precisely ξ. An associated problem is to consider a set with a convexity structure and a topology and find necessary and sufficient conditions for the existance of a linear structure on X such that X becomes a linear topological space with again ξ the collection of convex sets. 
Szafron, D. A.; Weston, J. H. An Internal Solution to the Problem of Linearization of a Convexity Space. Canadian mathematical bulletin, Tome 19 (1976) no. 4, pp. 487-494. doi: 10.4153/CMB-1976-073-0
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     title = {An {Internal} {Solution} to the {Problem} of {Linearization} of a {Convexity} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {487--494},
     year = {1976},
     volume = {19},
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     doi = {10.4153/CMB-1976-073-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1976-073-0/}
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