Boundary of a subset in a topological space ↩

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created: 2022-01-19 12:56:34
modified: 2022-01-19 16:13:28

Let be a topological space and .

Then the boundary of is defined by1

Thus, is closed and .

Points/elements

The following is true for every point of a closure2:

if and only if for every neighborhood of , and

Notation

  1. means the complement of on , i.e. .
    ↩

  2. Where denotes the empty set and is the complement of , i.e.
    ↩