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Open & Closed Sets

Chapter 4: Point Set Topology

Topology abstracts geometry by focusing on openness and closeness. Open Set: Every point in the set has a neighborhood completely contained within the set.
Closed Set: Contains all its boundary points.
Interact with the sets below to test their topological properties by probing with an "open ball" ($B_\epsilon$).

Hover over the canvas to probe the set.
Select a Set Topology:

An Interior Point is a point where you can find some radius string $\epsilon > 0$ such that the entire ball stays inside the set.
A Boundary Point is a point where any ball you draw contains points both inside and outside the set.

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