Open set

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Example: The blue circle represents the set of points (x, y) satisfying x2 + y2 = r2. The red disk represents the set of points (x, y) satisfying x2 + y2 < r2. The red set is an open set, the blue set is its boundary set, and the union of the red and blue sets is a closed set.

In set theory an open set is a set where all elements have the same properties.

Examples[change | change source]

The set (0,1) is open. If we choose a very small value, there will always be a small bubble which are all in the set (0,1).

If we choose a very small value h ∈ (0,1), we can make a bubble , in which all the values are in (0,1).


However, [0,1] is closed. If we choose the value 0, and choose a very small value k, 0-k ∉ [0,1], which means that it's closed.