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  "body": "\n## Summary\n\nThe disjoint union topology is the natural topology on a disjoint union of topological spaces.\nA set is open in it exactly when its part in each piece is open in that piece.\nIt makes the disjoint union the coproduct in the category of topological spaces.\nIt is the [[final topology|6ERJRRZK32]] for the inclusions of the pieces.\n\n## Explanations\n\n### L1 human\n\nPut several spaces side by side, with no overlap and no glue between them.\nEach piece keeps its own topology, and the pieces do not interact.\nA set is open when you can see it as an open set in each piece separately.\nFor example, the disjoint union of two copies of the interval $(0, 1)$ is a space with two separate parts.\nIt looks like the subspace $(0, 1) \\cup (2, 3)$ of the real line.\n",
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