Hello! I want to make sure I understand these definitions (mainly the difference between them), so please let me know if what I am saying is correct. So a ##\textbf{homeomorphism}## between 2 topological spaces, means that the 2 can be continuously deformed from one to another, while keeping a bijection between them (so a disk and a smaller disk inside it are homeomorphic, but a disk and a circle inside it are not). Then ##\textbf{homotopy}## means that 2 loops can be continuously deformed from one to another (not necessary bijectively - a circle and a point inside it are homotopic, for a simply connected space). Also, does homotopy applies just to loops, like 1 dimensional objects? And lastly the notion of ##\textbf{deformation retract}## means that 2 topologically spaces can be continuously transformed from one to another (not necessary in a bijective way - so a point is the deformation retract of a sphere). So a deformation retract is like midway between homotopy and homeomorphism (i.e. you can work not only with loops, but you don't need bijectivity)? Thank you!(adsbygoogle = window.adsbygoogle || []).push({});

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# I Homotopy Definitions

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