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математика
регулярная гомотопия
[klɑ:k'regjulə]
церковное выражение
иеромонах (у католиков)
математика
гомотопический класс
In the mathematical field of topology, a regular homotopy refers to a special kind of homotopy between immersions of one manifold in another. The homotopy must be a 1-parameter family of immersions.
Similar to homotopy classes, one defines two immersions to be in the same regular homotopy class if there exists a regular homotopy between them. Regular homotopy for immersions is similar to isotopy of embeddings: they are both restricted types of homotopies. Stated another way, two continuous functions are homotopic if they represent points in the same path-components of the mapping space , given the compact-open topology. The space of immersions is the subspace of consisting of immersions, denoted by . Two immersions are regularly homotopic if they represent points in the same path-component of .