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Identity component
also called Component group and has one more synonym

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  1. of a topological group G is the connected component G0 that contains the identity element e

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 12, 2009
  2. a term from mathematics

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 12, 2009
  3. G0 is a closed, normal subgroup of G. It is closed since components are always closed

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 12, 2009
  4. a subgroup since multiplication and inversion are continuous maps

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 12, 2009
  5. Moreover, for any continuous automorphism a of G we have It follows that G0 is normal in G. It is not always true that G0 is open in G. In fact, we may have G0 = e, in which case G is totally disconnected

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 12, 2009
  6. However, if G is a Lie group then G0 is open, since it contains a path-connected neighbourhood of e

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 12, 2009
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