nounfemininepl: homotopies
homotopia
1. In algebraic topology, a continuous deformation of one function or map into another, or the equivalence relation between topological spaces that can be continuously deformed into one another
Two continuous functions are homotopic if one can be continuously deformed into the other without breaking continuity.
Duas funções contínuas são homotópicas se uma pode ser continuamente deformada na outra sem quebrar a continuidade.
2. The continuous transformation itself that shows the equivalence between two topological structures
The homotopy between the circle and the figure-eight curve demonstrates their topological relationship.
A homotopia entre o círculo e a curva em forma de oito demonstra sua relação topológica.
Homotopy is a fundamental concept in algebraic topology, primarily used in academic and research contexts. The term is identical in both Brazilian Portuguese and European Portuguese mathematical communities, reflecting the universal nature of mathematical terminology. It is rarely encountered outside of mathematics education and research settings.
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