Nothing Special   »   [go: up one dir, main page]

Boundary (topology): Difference between revisions

Content deleted Content added
top: clarified tagged section about def in manifold theory, typed up the definitions in TeX
Line 11:
*the [[Closure (topology)|closure]] of ''<math>S</math>'' minus the [[Interior (topology)|interior]] of <math>S</math>: <math>\partial S := \bar{S} \setminus S^\circ</math>
*the intersection of the closure of ''<math>S</math>'' with the closure of its [[complement (set theory)|complement]]: <math>\partial S := \overline{S} \cap \overline{(X \setminus S)} </math>
*the set of points <math>p \in X</math> such that every [[neighborhood (topology)|neighborhood]] of <math>p</math> contains at least one point of ''<math>S</math>'' and at least one point not of ''<math>S</math>'': <math>\partial S := \{ p \in X: \mid \forall O \ni p,: O\cap S \neq \emptyset \,\text{ and }\, O \cap S^c \neq \emptyset \}</math>
 
== Examples ==