Oplysninger om | engelsk ord PATH-CONNECTED

Eksempler på brug af PATH-CONNECTED i en sætning

• It is tempting to try to simplify the definition of homotopy groups by omitting the base points, but this does not usually work for spaces that are not simply connected, even for path-connected spaces.
• For example, the cohomology ring of a path-connected H-space with finitely generated and free cohomology groups is a Hopf algebra.
• In detail, if q ∈ P is another chosen basepoint for the holonomy, then there exists a unique g ∈ G such that q ~ p g (since, by assumption, M is path-connected).
• Two path-connected topological spaces are sometimes said to be commensurable if they have homeomorphic finite-sheeted covering spaces.
• The arc, the n-sphere, and the Hilbert cube are examples of path-connected continua; the topologist's sine curve is an example of a continuum that is not path-connected.

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