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Zero-dimensional Polish spaces are a particularly convenient setting for descriptive set theory. Examples of such spaces include the Cantor space and Baire space. Hausdorff zero-dimensional spaces are precisely the subspaces of topological powers where = {,} is given the discrete topology.
Bioart is an art practice where artists work with biology, live tissues, bacteria, living organisms, and life processes. Using scientific processes and practices such as biology and life science practices, microscopy , and biotechnology (including technologies such as genetic engineering , tissue culture , and cloning ) the artworks are ...
Skills development in biological illustration can involve two-dimensional art, animation, graphic design, and sculpture (such as necessary in custom prosthetics). It is possible to work in biological illustration without a specific degree, but a degree will significantly enhance an illustrator's employment opportunities.
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.
In string theory and related theories (such as supergravity theories), a brane is a physical object that generalizes the notion of a zero-dimensional point particle, a one-dimensional string, or a two-dimensional membrane to higher-dimensional objects.
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.
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.