| Kiyosi Itô - Mathematics - 1993 - 1147 pages
...family ft of all closed sets satisfies (F). Given a subset A of A", the intersection A" of the family **of all closed sets containing A is called the closure of A,** and each point of A" is called an adherent point of A. The closure A" is the smallest closed set containing... | |
| Stephen C. Hirtle, Andrew U. Frank
...boundary and interior, respectively. Traditionally, o A is denned as the union of all open sets in A. The **intersection of all closed sets containing A is called the closure of A,** denoted by A. The exterior of A (wrt U) is U — A. dA is then defined as the intersection of the closure... | |
| J.K. Ghosh, R.V. Ramamoorthi - Mathematics - 2003 - 305 pages
...of closed sets is a closed set. For any set ACS, the smallest closed set containing A, which is the **intersection of all closed sets containing A, is called the closure of A** and will be denoted by A. Similarly A", the union of all open sets contained in A is called the interior... | |
| Keith Burns, Marian Gidea - Mathematics - 2005 - 400 pages
...Example 1.2.2 (iv). D The complement of an open set is said to be a closed set. Given a set ACX, the **intersection of all closed sets containing A is called the closure of A,** and is denoted by c\(A). The closure of a set is always a closed set. For a set A, the boundary set... | |
| Pavel Drabek, Jaroslav Milota - Mathematics - 2007 - 568 pages
...[35]. A subset F of a topological space X is called a closed set if X \ F is open. If ACX, then the **intersection of all closed sets containing A is called the closure of A** and is denoted by A, ie, J- is closed A dual notion is the interior (mtA) of A: int.A = (J SC.A Q is... | |
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