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  "body": "\n## Definition\n\nLet $V$ be a real [[vector space|000AYPA9AJ]] and let $x, y \\in V$.\nThe *open segment* between $x$ and $y$ is the set\n$$(x, y) = \\set{(1 - t) x + t y : t \\in \\R,\\ 0 \u003c t \u003c 1}.$$\n\n## Remarks\n\nExample: on the real line, $(0, 1)$ in this sense is the open interval of numbers strictly between $0$ and $1$; the point $1/4$ is in it with $t = 1/4$.\n\nNon-example: the endpoint $x$ of a [[line segment|VQ4Q2V45RP]] $[x, y]$ with $x \\ne y$ is not in $(x, y)$, since $(1 - t) x + t y = x$ forces $t (y - x) = 0$, so $t = 0$, which is not allowed.\n\nIf $x \\ne y$, then $(x, y) = [x, y] \\setminus \\set{x, y}$.\nIf $x = y$, then $(x, y) = \\set{x}$, so the open segment is not empty.\n",
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