Inclusion map

Under an inclusion mapping ( briefly also called inclusion ) is the mathematical function that embeds a subset into their basic amount.

For quantities and with the inclusion mapping is given by the mapping rule.

Sometimes the special arrow symbol is used to identify, to write then.

We speak of a true inclusion, if a proper subset of (ie: the inclusion mapping is not surjective ).

Properties

  • Each inclusion mapping is injective.
  • An arbitrary function f: A → B can be with respect to the concatenation of functions decompose as f = hog, where g is surjective and h is injective: Let C: = im f ⊆ B is the image set of f and g: A → C the function which corresponds to A f, that is g (x ) = f (x). For h: C → B we take the inclusion mapping.
  • F: A → B is an arbitrary function, and X is a subset of the defined set A, then it is understood from the limitation f | X f X to that of function g: X → B, which corresponds to X f. With the inclusion i: X → A can be written briefly as the restriction
  • Conversely, each inclusion mapping interpreted as restricting a suitable identity map:
  • Mathematical concept
  • Set theory
Mathematics
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