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- Affine line with doubled origin
- Clopen determinacy with terminal losses
- Clopen up-set
- Compact Hausdorff topology on ultrafilters
- Cone on an infinite coinfinite ground set
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- Cylinder set
- Ellentuck topology
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- p-adic measure
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- Quasicomponent
- Strong zero-dimensionality
- Topological disjoint union
- Totally separated space
- Ultrametric space
- Zero-dimensional space
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In topology, a set is called **clopen** if it is both **closed** and **open**. To understand this concept, we need to clarify what it means for a set to be open and closed: 1. A set \( U \) in a topological space is **open** if, for every point \( x \) in \( U \), there exists a neighborhood of \( x \) that is entirely contained within \( U \).