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Integrally convex set
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<p>An integrally convex set is the <a href="/facts/Discrete_geometry/Ixnl3GBc">discrete geometry</a> analogue of the concept of <a href="/facts/Convex_set/vdAuJRJl">convex set</a> in geometry. </p><p>A subset <i>X</i> of the integer grid Z n {\displaystyle \mathbb {Z} ^{n}} is integrally convex if any point <i>y</i> in the <a href="/facts/Convex_hull/D4Id3JDS">convex hull</a> of <i>X</i> can be expressed as a <a href="/facts/Convex_combination/YSDu46RI">convex combination</a> of the points of <i>X</i> that are "near" <i>y</i>, where "near" means that the distance between each two coordinates is less than 1. </p>