topological embedding
[/ˌtɑːpəˈlɑːdʒɪkəl ˈɛmbɛdɪŋ/]
nounpl: topological embeddings
imersão topológica
1. In mathematics and topology, a continuous injective function between topological spaces that is also a homeomorphism onto its image with the subspace topology.
The topological embedding of a circle into three-dimensional space preserves all topological properties of the original space.
A imersão topológica de um círculo no espaço tridimensional preserva todas as propriedades topológicas do espaço original.
2. A map that allows one topological space to be included within another space such that the original space's topology is preserved.
We can use a topological embedding to show that the open interval (0,1) is homeomorphic to the real line.
Podemos usar uma imersão topológica para mostrar que o intervalo aberto (0,1) é homeomorfo à reta real.
This is a specialized term primarily used in academic mathematics, particularly in topology courses and research. It is a technical term not commonly encountered outside of mathematical contexts in either Brazilian Portuguese or English-speaking countries. The concept is fundamental to modern topology and differential geometry.
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