homotopic การใช้

• Next, any map on the M鯾ius group is homotopic to the identity.
• From this point of view, is a homotopic.
• Requiring that two embeddings be isotopic is a stronger requirement than that they be homotopic.
• In particular we find that vector bundles inducing homotopic maps to the Grassmannian are isomorphic.
• The relation of being homotopic is an equivalence relation on paths in a topological space.
• By our assumption, and are piecewise smooth homotopic, there are the piecewise smooth homogony
• This means that we can consider homotopic equivalence class of paths to have different weighting factors.
• But the definition of homotopic relies on a notion of continuity, and hence a topology.
• Isotopy invariance of the linking number is automatically obtained as the degree is invariant under homotopic maps.
• Merker, for instance, argues that the homotopic connectivity of sensory pathways does the necessary work.
• Hopf proved that the Hopf map has Hopf invariant 1, and therefore is not null-homotopic.
• Two mappings are "'homotopic "'if one can be continuously deformed into the other.
• At any rate, we can see that there are gauge transformations U homotopic to the trivial gauge transformation.
• The "'Borel conjecture "'states that the map f is homotopic to a homeomorphism.
• A weak form of Tutte's homotopy theorem states that any closed path is homotopic to the trivial path.
• The Hawaiian earring is not simply connected, since the loop parametrising any circle is not homotopic to a trivial loop.
• Under what conditions is f homotopic to the identity \ text { id } _ T : T \ to T.
• With Jack Snoeyink he extended the algorithms for simple polygons to compute homotopic shortest paths among polygonal obstacles in the plane.
• The gluing map is homotopic to the identity map on the circle and so the complex is homotopy equivalent to the disc.
• In this sense, the homotopy pushouts treats homotopic spaces as well as the ( ordinary ) pushout does with homeomorphic spaces.