Sequentially Compact Space

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, more specifically general topology and metric topology, a compact space is an abstract mathematical space in which, intuitively, whenever one takes an infinite number of "steps" in the space, eventually one must get arbitrarily close to some other point of the space. Thus a closed and bounded subset (such as a closed interval or rectangle) of a Euclidean space is compact because ultimately one's steps are forced to "bunch up" near a point of the set, a result known as the Bolzano-Weierstrass theorem, whereas Euclidean space itself is not compact because one can take infinitely many equal steps in any given direction without ever getting very close to any other point of the space.