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Compact Hausdorff 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 by making precise the idea of a space having no "punctures" or "missing endpoints", i.e. that the space not exclude any ''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 ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topologic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact
Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to: * Interstate compact * Blood compact, an ancient ritual of the Philippines * Compact government, a type of colonial rule utilized in British North America * Compact of Free Association whereby the sovereign states of the Federated States of Micronesia, the Republic of the Marshall Islands and the Republic of Palau have entered into as associated states with the United States. * Mayflower Compact, the first governing document of Plymouth Colony * United Nations Global Compact * Global Compact for Migration, a UN non-binding intergovernmental agreement Mathematics * Compact element, those elements of a partially ordered set that cannot be subsumed by a supremum of any directed set that does not already contain them * Compact operator, a linear operator that takes bounded subsets to relatively compact subsets, in functional analysis * Compact space, a topological space such tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
