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.
Synonyms / Sinônimos
topological injectionembeddinghomeomorphic embeddingcontinuous injection
Antonyms / Antônimos
topological separationnon-injective mapping

Regional Variations

General Brazilian
imersão topológica
Standard terminology used in Brazilian mathematics education and research
São Paulo
imersão topológica
Used in academic and university contexts, particularly in USP and UNICAMP
Portugal
imersão topológica
Used in Portuguese academic mathematics, sometimes also 'mergulho topológico'

Related Words

homeomorphismtopologycontinuous functionsubspace topologyinjective functiontopological space
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