Homotopic

Word HOMOTOPIC
Character 9
Hyphenation N/A
Pronunciations N/A

Definitions and meanings of "Homotopic"

What do we mean by homotopic?

Here you will find one or more explanations in English for the word homotopic. Define homotopic, homotopic synonyms, homotopic pronunciation, homotopic translation, English dictionary definition of homotopic.

Synonyms and Antonyms for Homotopic

  • Synonyms for homotopic
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  • Antonyms for homotopic
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The word "homotopic" in example sentences

Let us pass to another analogy for now: a particle moves around in a topological space, and we wish to describe its path as simply as possible, in such a way that two paths that may be deformed into each other (i.e., are homotopic), are given the same description. ❋ Unknown (2009)

A space is termed simply connected if every loop in the space is homotopic to a constant loop. ❋ Unknown (2009)

If a pair of nuclei can be interchanged by rotation about an axis of symmetry of the molecule then they are chemically equivalent and are called homotopic. e.g. the pair of protons in dichloromethane are chemically equivalent. ❋ Unknown (2009)

To prove carefully that paths going around the circle different numbers of times are not homotopic to each other requires a bit more machinery than is developed in this article. ❋ Unknown (2009)

This stretching can't pass over a hole, so a characterization of homotopic paths yields a characterization of holes. topological space X, the fundamental group is an associated algebraic object which describes the paths that are not homotopic, and hence describes the set of "holes" in the space. ❋ PatrickD (2009)

Two paths are said to be homotopic if one can be continuously deformed/moved/stretched into the other. ❋ Unknown (2009)

In a simply connected space, all loops are homotopic and thus represent a single homotopy class, and so the fundamental group is the trivial group, with only one element. ❋ Unknown (2009)

Two paths γ0, γ1 are said to be homotopic if there is a continuous function ❋ Unknown (2009)

Let us pass to another analogy for now: a particle moves around in a topological space, and we wish to describe its path as simply as possible, and such that two paths that may be deformed into each other (i.e., are homotopic), are given the same description. ❋ Unknown (2009)

Cross Reference for Homotopic

What does homotopic mean?

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