homotopic

Two mappings are homotopic if one can be continuously deformed into the other.

Then if and only if f and g are homotopic.

It should be strongly remarked that this does not have anything in common with the techniques of homotopic continuation.

Because all sections of are homotopic, the homotopy class of is unique.

Homotopic atoms are always identical, in any environment.

However, it can be shown that concatenation and pointwise multiplication are homotopic.

By taking k big enough, we see that γ is homotopic, with respect to the base point, to the constant map.

Homotopic groups in a chemical compound are equivalent groups.

Next, the Möbius group is connected, so any map is homotopic to the identity.

A simplicial approximation is homotopic to the map it approximates.

That is, if is homotopic to , then their induced maps are the same.

The Borel conjecture states that the map is homotopic to a homeomorphism.

Depending on the relationship, such groups can be heterotopic, homotopic, enantiotopic, or diastereotopic.

If the complexes and are homotopic and , then .

Two immersions are regularly homotopic if they represent points in the same path-component of .

The set of loops at a particular base point can be studied without regarding homotopic loops as equivalent.

That these configuration spaces are not homotopic was detected by Massey products in their respective universal covers.

Equivalence classes of timelike homotopic curves define their own fundamental group, as noted by Smith (1967).

Being homotopic is an equivalence relation on the set of all continuous functions from X to Y.

The relation of being homotopic is an equivalence relation on paths in a topological space.

Homotopy: Homotopic maps induce the same map in homology.

But the definition of homotopic relies on a notion of continuity, and hence a topology.

Merker, for instance, argues that the homotopic connectivity of sensory pathways does the necessary work.

If a gauge transformation isn't homotopic to the identity, it is called a large gauge transformation.

Two embeddings are isotopic if they are homotopic through embeddings.