General topology Ordered spaces and set-theoretic topology Concept
Linear continuum
Summary
A linear continuum is a totally ordered set with more than one element that has no gaps and no jumps. Every nonempty subset bounded above has a supremum, and between any two elements lies a third. The real line is the model example. In the order topology, every linear continuum is connected, and so are its intervals.
Further reading
About this page
| Tag | MM0QPT0GT0 |
|---|---|
| URI | m2://MM0QPT0GT0 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 54F05, 06A05 |
| Specializes | Total order |
| Same as | |
| Changed | 2 November 2026 |
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