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Finest Topology
In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can be used for comparison of the topologies. Definition A topology on a set may be defined as the collection of subsets which are considered to be "open". An alternative definition is that it is the collection of subsets which are considered "closed". These two ways of defining the topology are essentially equivalent because the complement of an open set is closed and vice versa. In the following, it doesn't matter which definition is used. Let ''τ''1 and ''τ''2 be two topologies on a set ''X'' such that ''τ''1 is contained in ''τ''2: :\tau_1 \subseteq \tau_2. That is, every element of ''τ''1 is also an element of ''τ''2. Then the topology ''τ''1 is said to be a coarser (weaker or smaller) topology than ''τ''2, and ''τ''2 is said to be a finer (stronger or larger) topology than ''τ''1. There are some authors, especially ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strong Topology (polar Topology)
Strong may refer to: Education * The Strong, an educational institution in Rochester, New York, United States * Strong Hall (Lawrence, Kansas), an administrative hall of the University of Kansas * Strong School, New Haven, Connecticut, United States, an overflow school for district kindergartners and first graders Music Albums * ''Strong'' (Anette Olzon album), 2021 * ''Strong'' (Arrested Development album), 2010 * ''Strong'' (Michelle Wright album), 2013 * ''Strong'' (Thomas Anders album), 2010 * ''Strong'' (Tracy Lawrence album), 2004 * ''Strong'', a 2000 album by Clare Quilty Songs * "Strong" (London Grammar song), 2013 * "Strong" (One Direction song), 2013 * "Strong" (Robbie Williams song), 1998 * "Strong", a song by After Forever from ''Remagine'' * "Strong", a song by Audio Adrenaline from '' Worldwide'' * "Strong", a song by LeAnn Rimes from '' Whatever We Wanna'' * "Strong", a song by London Grammar from ''If You Wait'' * "Strong", a song by Will Hoge from '' N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
