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  "body": "\n## Summary\n\nA sequential space is a topological space whose topology is determined by its convergent sequences.\nA set is closed in it exactly when it contains the limits of all its convergent sequences.\nEvery [[first-countable space|0CP5NDD21C]], in particular every metric space, is sequential.\nIn a sequential space, sequences are enough to test closedness and continuity, so nets or filters are not needed.\n\n## Explanations\n\n### L1 human\n\nIn a metric space, you can decide whether a set is closed by checking sequences: a closed set keeps the limits of its sequences.\nIn a general space this test can fail, because sequences may be too short to reach some points.\nSequential spaces are the spaces where the sequence test still works.\nFor example, in $\\R$ the set $(0, 1]$ is not closed, and the sequence $1/n$ in it shows this, because its limit $0$ is outside.\n",
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