Mathematics › Topology
Poset representing certain properties of a polytope
In mathematics, an abstract polytope is an algebraic partially ordered set which captures certain combinatorial properties of a traditional polytope without specifying purely geometric properties such as the position of vertices.
Mathematics › Topology
Concept in topology
In geometric topology and differential topology, an (n + 1)-dimensional cobordism W between n-dimensional manifolds M and N is an h-cobordism (the h stands for homotopy equivalence) if the inclusion maps M↪WandN↪W are homotopy equivalences.
Mathematics › Topology
Topological property
In algebraic topology, homotopical connectivity is a property describing a topological space based on the dimension of its holes. In general, low homotopical connectivity indicates that the space has at least one low-dimensional hole.
Mathematics › Topology
Mathematical group of the homotopy classes of loops in a topological space
In the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of the topological space.
Mathematics › Topology
Property of topological spaces
In topology, a topological space X is called a compactly generated space or k-space if its topology is determined by compact spaces in a manner made precise below.
Mathematics › Topology
In mathematics, in the field of differential geometry, the Yamabe invariant, also referred to as the sigma constant, is a real number invariant associated to a smooth manifold that is preserved under diffeomorphisms. It was first written down independently by O. Kobayashi and R.
Mathematics › Topology
Quotient of a weakly contractible space by a free action
In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e., a topological space all of whose homotopy groups are trivial) by a proper free action of G.
Mathematics › Topology
Property of topological spaces
In topology and other branches of mathematics, a topological space X is locally connected if every point admits a neighbourhood basis consisting of open connected sets.
Mathematics › Topology
"Small" subset of a topological space
In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that is a countable union of subsets whose closures have empty interior.
Mathematics › Topology
Function that is discontinuous at rationals and continuous at irrationals
Thomae's function is a real-valued function of a real variable that can be defined as: f(x)={1qif x=pq(x is rational), with p∈ℤ and q∈ℕ coprime0if x is irrational.
Mathematics › Topology
Mathematical set whose closure has empty interior
In mathematics, a subset of a topological space is called nowhere dense or rare if its closure has empty interior. In a very loose sense, it is a set whose elements are not tightly clustered (as defined by the topology on the space) anywhere.
Mathematics › Topology
Knots have been used for basic purposes such as recording information, fastening and tying objects together, for thousands of years. The early significant stimulus in knot theory would arrive later with Sir William Thomson (Lord Kelvin) and his vortex theory of the atom.
