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Stone–Čech Remainder
In mathematics, the Stone–Čech remainder of a topological space ''X'', also called the corona or corona set, is the complement (set theory), complement of the space in its Stone–Čech compactification β''X''. A topological space is said to be σ-compact space, σ-compact if it is the union of Countable set, countably many compact space, compact subspaces, and locally compact space, locally compact if every point has a neighbourhood (mathematics), neighbourhood with compact closure (topology), closure. The Stone–Čech remainder of a σ-compact and locally compact Hausdorff space is a sub-Stonean space, i.e., any two open set, open σ-compact disjoint sets, disjoint subsets have disjoint compact closures. See also *Corona theorem *Corona algebra, a non-commutative analogue of the corona set. References *{{Citation , last1=Grove , first1=Karsten , last2=Pedersen , first2=Gert Kjærgård , title=Sub-Stonean spaces and corona sets , doi=10.1016/0022-1236(84)90028- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
