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A space whose elements are equivalence classes of pairs <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026350/c0263501.png" /> of convex sets (cf. [[Convex set|Convex set]]) in a locally convex linear topological space. The pair <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026350/c0263502.png" /> is treated as the  "difference"  <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026350/c0263503.png" />, pairs <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026350/c0263504.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026350/c0263505.png" /> being equivalent by definition if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026350/c0263506.png" />, where addition of sets is understood to mean the closure of the vector sum. Addition, subtraction, multiplication by a scalar, and a topology are introduced in the space of convex sets, that space becoming thereby a locally convex topological space. Also the concept of partial ordering is introduced, which is analogous to inclusion of sets. Linear spaces of convex sets are also considered in non-locally convex linear spaces.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A.G. Pinsker,   "The space of convex sets of a locally convex space"  ''Trudy Leningrad. Inzh.-Ekon. Inst.'' , '''63'''  (1966)  pp. 13–17  (In Russian)</TD></TR></table>