Deformation retracts

Definition. (Deformation retract(ion)s)

Let $A\subset X$ , write $A\xrightarrow i X$ .

\begin{aligned} H(x,0) &= x && \forall x\in X\\ \htmlClass{defo-H2}{H(x,1)} &\htmlClass{defo-H2}{\in A} && \htmlClass{defo-H2}{\forall x\in X}\\ \htmlClass{defo-H3}{H(a,1)} &\htmlClass{defo-H3}{= a} && \htmlClass{defo-H3}{\forall a\in A} \end{aligned}

\begin{aligned} X &= \bigcup_{n\in\N} L_n & L_0 &= \text{line segment from \htmlClass{p0}{origin} to } \htmlClass{p10}{(1,0)}\\ && L_n &= \text{line segment from \htmlClass{p0}{origin} to } (1,\tfrac1n) \end{aligned}