A **realcompact space** is a specific type of topological space that has particular properties related to compactness and the behavior of real-valued continuous functions. To define realcompactness, we first need to understand a few concepts: 1. **Compact Space**: A topological space is compact if every open cover of the space has a finite subcover. Essentially, this means that, intuitively, a space is "small" in some sense.
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