Search results
Results From The WOW.Com Content Network
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. [1] A graphical illustration of a zero-dimensional space is a point. [2]
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, [1] or its generalization to other kinds of mathematical spaces.As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist; conversely ...
The simplest example of a vector space is the trivial one: {0}, which contains only the zero vector (see the third axiom in the Vector space article). Both vector addition and scalar multiplication are trivial. A basis for this vector space is the empty set, so that {0} is the 0-dimensional vector space over F.
Zero (usually styled as ZERO) was an artist group founded in the late 1950s in Düsseldorf by Heinz Mack and Otto Piene. Piene described it as "a zone of silence and of pure possibilities for a new beginning". [1] In 1961 Günther Uecker joined the initial founders. ZERO became an international movement, with artists from Germany, the ...
Over a commutative ring, a trivial algebra is simultaneously a zero module. The trivial ring is an example of a rng of square zero. A trivial algebra is an example of a zero algebra. The zero-dimensional vector space is an especially ubiquitous example of a zero object, a vector space over a field with an empty basis. It therefore has dimension ...
The first formal definition of covering dimension was given by Eduard Čech, based on an earlier result of Henri Lebesgue. [4] A modern definition is as follows. An open cover of a topological space X is a family of open sets U α such that their union is the whole space, U α = X.
Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.
Such a space is called a Baire space of weight and can be denoted as (). [1] With this definition, the Baire spaces of finite weight would correspond to the Cantor space . The first Baire space of infinite weight is then B ( ℵ 0 ) {\displaystyle B(\aleph _{0})} ; it is homeomorphic to ω ω {\displaystyle \omega ^{\omega }} defined above.