# If Ā = ∩ F then show that A ⊆ Ā and Ā is the smallest closed set that contains A?

hi

my question is:

The closure of A is denoted by Ā. Ā = ∩ F, where the intersection is taken

over all the closed sets F that contain A.

show:

1- A ⊆ Ā

2- Ā is the smallest closed set that contains A

my question is:

The closure of A is denoted by Ā. Ā = ∩ F, where the intersection is taken

over all the closed sets F that contain A.

show:

1- A ⊆ Ā

2- Ā is the smallest closed set that contains A

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