embedded submanifold
[ɛmˈbɛdɪd ˌsʌbməˈnɪfoʊld]
nounpl: embedded submanifolds
subvariedade imersa
1. A submanifold that is realized as a subset of a manifold through an injective immersion that is also a topological embedding, preserving the submanifold structure within the ambient manifold
A circle is an embedded submanifold of the plane when it is realized as a smooth curve without self-intersections.
Um círculo é uma subvariedade imersa do plano quando realizado como uma curva suave sem auto-interseções.
2. In differential geometry, a smooth manifold M is an embedded submanifold of a manifold N if there exists a smooth injective immersion that is also a homeomorphism onto its image with the subspace topology
The sphere is an embedded submanifold of three-dimensional Euclidean space.
A esfera é uma subvariedade imersa do espaço euclidiano tridimensional.
This is specialized mathematical terminology used primarily in academic and research contexts within differential geometry and topology. It appears frequently in graduate-level mathematics courses and research publications. The term is used identically in both Brazilian Portuguese and European Portuguese mathematical literature, reflecting the universal nature of mathematical terminology across Portuguese-speaking academic communities.
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