Mathematics MOC

Embedding

An embedding is an injective homomorphism which induces an isomorphism with its image. See Regular monomorphism for a categorical generalization.

Topology

An embedding is an injective continuous map 𝑓 :π‘Œ β†ͺ𝑋 such that it would be impossible for π‘Œ to have a coarser topology, i.e. the topology of π‘Œ is the same as the subspace topology induced by 𝑓.1 #m/def/topology Equivalenly, the open sets in π‘Œ are precisely the preΓ―mages of the open sets in 𝑋.

Differential topology

A πΆπ‘˜ embedding of π‘Œ in 𝑋 is a πΆπ‘˜ diffeomorphism between π‘Œ and a submanifold of 𝑋. #m/def/geo/diff

Others

#state/tidy | #lang/en | #SemBr

Footnotes

  1. 2020, Topology: A categorical approach, 26 ↩