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  "body": "\n## Summary\n\nA continuous lattice is a complete lattice in which every element is the supremum of the elements [[way below|RDM7J5J9HQ]] it.\nContinuous lattices were introduced by Dana Scott as models for the semantics of programming languages, and they connect order theory with topology.\nEvery [[algebraic lattice|3J0BTXSCVN]] is continuous, and so is the unit interval $[0, 1]$.\n\n## Explanations\n\n### L1 human\n\nAn element $x$ is way below $y$ when $x$ is reached by every increasing approach to $y$ before the approach is finished.\nIn $[0, 1]$, the number $x$ is way below $y$ when $x \u003c y$, or $x = 0$.\nA continuous lattice is one where every element can be approximated from below by elements way below it.\nSo $[0, 1]$ is continuous: each $y \u003e 0$ is the supremum of the numbers $x \u003c y$.\nIn an algebraic lattice the approximating elements can be taken compact, that is, \"finite\".\n",
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