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  "body": "\n## Summary\n\nA pseudocompact space is a [[topological space|0CQHFPGJ45]] on which every continuous real-valued function is bounded.\nIt keeps one of the most used consequences of [[compactness|0TVJZYB6SH]], the boundedness of continuous functions, without asking for finite subcovers.\nEvery compact space and every [[countably compact space|S3N3CHZV89]] is pseudocompact.\nFor [[metric spaces|0VKD1TP7F3]] the notion gives nothing new: a metric space is pseudocompact exactly when it is compact.\n\n## Explanations\n\n### L1 human\n\nOn a closed bounded interval, a continuous function cannot run off to infinity.\nA pseudocompact space is a space where this good behaviour holds for every continuous function into the real line.\nThe real line itself is not pseudocompact, because the function $f(x) = x$ is continuous and unbounded.\nThe interval $[0, 1]$ is pseudocompact, because it is compact.\n",
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