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. Simply put, an open set is a set that does not include its edges or endpoints. For each point in the set, you can make a bubble around that point, such that all points in the bubble are also in the set.
On the other hand, a closed set includes all its edges or endpoints. A set that includes some of its edges or endpoints is neither open nor closed.
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