ASL STEM

Path Homotopy Sign Video

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Definition

Two paths f and g. mapping the interval I=[0, 1] into X, are said to be path homotopic if they have the same initial point x_0 and the same final point x_1, and if there is a continuous map F: IxI -> X such that F(s, 0)=f(s) and F(s, 1)=g(s), F(0, t)=x_0 and F(1, t)=x_1, for each s in I and each t in I. We call F a path homotopy between f and g.

Source: Topology (second edition) by James R. Munkres

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> Mathematics

> Algebraic Topology

> Path Homotopy

+ The Jordan Curve Theorem *

+ Triangulable *

+ Brouwer Fixed Point Theorem *

+ Nulhomotopy *

- Path Homotopy *

+ Straight Line Homotopy *

+ Positive Linear Map *

+ Monomorphism *

+ Epimorphism *

+ Fundamental Group *

+ First Homotopy Group *

+ Covering Map *

+ Simple Connectedness *

+ Evenly Covered *

+ Local Homeomorphism *

+ Lifting Correspondence *

+ No Retraction Theorem *

+ Borsuk Ulam Theorem *

+ The Bisection Theorem *

+ Homotopy Extension Lemma *

+ Borsuk Lemma *

+ Antipode Preserving *

+ Deformation Retract *

+ Deformation Retraction *

+ Doubly Punctured Plane *

+ Homotopy Equivalences *

+ Homotopy Inverse *

+ Homotopy Type *

+ Projective Plane *

+ Nulhomotopy Lemma *

+ Simple Closed Curve *

+ The Jordan Separation Theorem *

+ Invariance Of Domain *

+ Schoenflies Theorem *

+ Linear Graph *

+ Theta Space *

+ Free Homotopy *

+ Simple Loop *

+ Free Abelian Group *

+ Free Product *

+ External Free Product *

+ External Direct Sum *

+ Least Normal Subgroup *

+ System Of Free Generators *

+ Torsion Subgroup *

+ Betti Number *

+ Elementary Divisors *

+ Relations Subgroup *

+ Presentation *

+ Curved Triangle *

+ Complete Set Of Relations *

+ Seifert Van Kampen Theorem *

+ Wedge Of The Circles *

+ Homology Group *

+ Projective Type *

+ The Classification Theorem *

+ Triangulation *

+ Universal Covering Space *

+ Covering Transformation *

+ Orbit Space *

+ Properly Discontinuous *

+ Semilocally Simply Connected *

+ Euler Number *

+ Covering Space *

+ Winding Number *

* video needed

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