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For mathematical completeness, consider adding:
fn interior(&self) -> Interval<T> // Topological interior fn closure(&self) -> Interval<T> // Topological closure fn boundary(&self) -> Interval<T> // Topological boundary
1. Interior (Topological Interior) The interior of a set consists of all points that have a neighborhood entirely contained within the set.
2. Closure (Topological Closure) The closure includes all points that can be approximated by points in the set.
3. Boundary (Topological Boundary) The boundary consists of points where every neighborhood contains both points in and out of the set.
Some important mathematical properties these functions would satisfy:
The main implementation challenge is that boundary() naturally wants to return a set of discrete points rather than an interval. This suggests either:
boundary()
The text was updated successfully, but these errors were encountered:
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Proposal
For mathematical completeness, consider adding:
1. Interior (Topological Interior)
The interior of a set consists of all points that have a neighborhood entirely contained within the set.
2. Closure (Topological Closure)
The closure includes all points that can be approximated by points in the set.
3. Boundary (Topological Boundary)
The boundary consists of points where every neighborhood contains both points in and out of the set.
Properties
Some important mathematical properties these functions would satisfy:
Challenges
The main implementation challenge is that
boundary()
naturally wants to return a set of discrete points rather than an interval. This suggests either:The text was updated successfully, but these errors were encountered: