This is the open-boundary case of an interval.
An open interval in the real line is a set (a,b)={x:a<x<b}, allowing either endpoint to be infinite.
A nondegenerate interval contains more than one point; for an interval with finite endpoints, this means that its endpoints are distinct.
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- A derivative has no removable discontinuity
- Cauchy mean value theorem
- Circle and interval are not homeomorphic
- Closed real interval
- Closed subgroup
- Compact space
- Connected space
- Connected subset
- Connected subset of the real line
- Continuous image of a compact space
- Continuous map
- Continuous maps from an infinite cofinite space to a Hausdorff space are constant
- Degree ordering in an orthonormal polynomial basis
- Extreme value theorem
- Heine-Borel theorem
- Homeomorphism
- Horseshoe for an interval map
- Implicit solution
- Intermediate value theorem
- Interval exactness produces a horseshoe
- Local uniform Cauchy control for pointwise convergent continuous functions
- Mean value theorem
- Nested intervals
- Nested interval theorem
- Open arc
- Orthogonality forces many interior zeros
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