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Hausdorff and Non-Hausdorff Spaces
- 1. Hausdorff and Non-Hausdorff Spaces Mayra Ibarra MATH101
- 4. T 2 : If a, b ϵ X, there exist disjoint open sets O a and O b containing a and b respectively.
- 6. T 3 : If A is a closed set and b is a point not in A, there exist disjoint open sets O A and O b containing A and b respectively. X
- 7. T 4 : If A and B are disjoint closed sets in X, there exist disjoint open sets O A and O B containing A and B respectively X
- 8. T 5 : If A and B are separated sets in X, there exist disjoint open sets O A and O B containing A and B respectively
- 19. If X is Hausdorff and (S n ) is a sequence in X that converges to a point s Є X, and if y is an accumulation point of the set {S n | n = 1, 2, . . .}, then s = y.