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[[Image:Vector norms.svg|frame|right|The unit ball in the middle figure is strictly convex, while the other two balls are not (they contain a line segment as part of their boundary).]]
In [[mathematics]], a '''strictly convex space''' is a [[normed vector space|normed]] [[topological vector space]] (''V'', || ||) for which the [[unit ball]] is a strictly [[convex set]]. Put another way, a strictly convex space is one for which, given any two points ''x'' and ''y'' in the [[boundary (topology)|boundary]] ∂''B'' of the unit ball ''B'' of ''V'', the [[affine line]] ''L''(''x'', ''y'') passing through ''x'' and ''y'' meets ∂''B'' ''only'' at ''x'' and ''y''. Strict convexity is somewhere between an [[inner product space]] (all inner product spaces are strictly convex) and a general [[normed space]] (all strictly convex normed spaces are normed spaces) in terms of structure. It also
==Properties==
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