Compact space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all limiting values of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval [0,1] would be compact. Similarly, the space of rational numbers
Compact space - Wikipedia Jump to content From Wikipedia, the free encyclopedia "Compactness" redirects here. For other uses, see Compactness (disambiguation) . Type of mathematical space Per the compactness criteria for Euclidean space as stated in the Heine–Borel theorem , the interval A = (−∞, −2] is not compact because it is not bounded. The interval C = (2, 4) is not compact because it is not closed (but bounded). The interval B = [0, 1] is compact because it is both closed and bounded. In mathematics , especially general topology and mathematical analysis , compactness is a property of a
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