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Open Immersion


An open immersion is a morphism of schemes j:U->X that identifies U with an open subscheme of X. It induces a homeomorphism onto an open set of X, and its map on structure sheaves is the restriction map.

Every open immersion is a scheme immersion. It is the scheme-theoretic analogue of including an open subset into a topological space.


See also

Closed Immersion, Open Set, Scheme Immersion, Subscheme

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References

Grothendieck, A. and Dieudonné, J. "Éléments de géométrie algébrique. I. Le langage des schémas." Publ. Math. IHES 4, 5-228, 1960. https://doi.org/10.1007/BF02684778.The Stacks Project Authors. "Immersions of Schemes." §26.10 in The Stacks Project, Tag 01IM, 2026. https://stacks.math.columbia.edu/tag/01IM.

Cite this as:

Weisstein, Eric W. "Open Immersion." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OpenImmersion.html

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