Compact space

Compactness is a property of mathematics that seeks to generalize the idea of closed and bounded sets. A compact space has no gaps or missing parts, and it includes all the limit points. For example, the interval ${\displaystyle (0,1)}$ is not compact because the closure points 0 and 1 are not included of this interval. But ${\displaystyle [0,1]}$ is compact because its both closure points are included to this interval.

A compact space B and two non-compact spaces A (not bounded) and C (not closed)