Matches in DBpedia 2014 for { ?s ?p In topology, the suspension SX of a topological space X is the quotient space:of the product of X with the unit interval I = [0, 1]. Intuitively, we make X into a cylinder and collapse both ends to two points. One views X as "suspended" between the end points. One can also view the suspension as two cones on X glued together at their base (or as a quotient of a single cone).Given a continuous map there is a map defined by This makes into a functor from the category of topological spaces into itself. In rough terms S increases the dimension of a space by one: it takes an n-sphere to an (n + 1)-sphere for n ≥ 0.Note that is homeomorphic to the join where is a discrete space with two points.The space is sometimes called the unreduced, unbased, or free suspension of , to distinguish it from the reduced suspension described below.The suspension can be used to construct a homomorphism of homotopy groups, to which the Freudenthal suspension theorem applies. In homotopy theory, the phenomena which are preserved under suspension, in a suitable sense, make up stable homotopy theory.. }
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- Suspension_(topology) abstract "In topology, the suspension SX of a topological space X is the quotient space:of the product of X with the unit interval I = [0, 1]. Intuitively, we make X into a cylinder and collapse both ends to two points. One views X as "suspended" between the end points. One can also view the suspension as two cones on X glued together at their base (or as a quotient of a single cone).Given a continuous map there is a map defined by This makes into a functor from the category of topological spaces into itself. In rough terms S increases the dimension of a space by one: it takes an n-sphere to an (n + 1)-sphere for n ≥ 0.Note that is homeomorphic to the join where is a discrete space with two points.The space is sometimes called the unreduced, unbased, or free suspension of , to distinguish it from the reduced suspension described below.The suspension can be used to construct a homomorphism of homotopy groups, to which the Freudenthal suspension theorem applies. In homotopy theory, the phenomena which are preserved under suspension, in a suitable sense, make up stable homotopy theory.".