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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 physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime [nb 1] that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space.
The dimension of a vector space is the number of vectors in any basis for the space, i.e. the number of coordinates necessary to specify any vector. This notion of dimension (the cardinality of a basis) is often referred to as the Hamel dimension or algebraic dimension to distinguish it from other notions of dimension.
0th or zeroth, an ordinal for the number 0; 0th dimension, a topological space; 0th element, of a data structure in computer science; 0th law of Thermodynamics; Zeroth (software), deep learning software for mobile devices
One, which would now be called Serre duality, interprets the () term as a dimension of a first sheaf cohomology group; with () the dimension of a zeroth cohomology group, or space of sections, the left-hand side of the theorem becomes an Euler characteristic, and the right-hand side a computation of it as a degree corrected according to the ...
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence of Betti numbers is 0 from some point onward (Betti numbers vanish above the dimension of a space), and they ...
The Kervaire invariant problem, about the existence of manifolds of Kervaire invariant 1 in dimensions 2 k − 2 can be reduced to a question about stable homotopy groups of spheres. For example, knowledge of stable homotopy groups of degree up to 48 has been used to settle the Kervaire invariant problem in dimension 2 6 − 2 = 62.
If the maximum dimension of a chain is k, then we get the following sequence of groups: It can be proved that any boundary of a (k+1)-dimensional cell is a k-dimensional cycle. In other words, for any k , im ∂ k + 1 {\displaystyle \operatorname {im} \partial _{k+1}} (the group of boundaries of k +1 elements) is contained in ker ∂ k ...