Why does the boundary of mobius strip wrap twice around core circle but not any other line? A space $X$ deformation retracts onto a subspace $A$ if there exists continuous map $F:X\times [0,1]\rightarrow X$ such that $F(x,0)=x,F(x,1)\in A,F(a,t)=a$ $\forall a\in A$.
The mobius strip deformation retracts onto its core circle. But I don't understand how, under this deformation retraction, 


*

*The boundary circle wraps twice around the core circle

*Any other line wraps only once around the core circle


I think 1 happens because at each step of the deformation retraction, the boundary goes around twice and so in the final step (i.e. $t=1$) it just becomes twice the circle. But I see this reason working equally well for any other line. After all, none of the lines actually coincide with the central line until the last step. 
Any help would be appreciated.

I believe this picture answers your question. Every line that isn't the centre will wrap around twice. So "2. Any other line wraps only once around the core circle" isn't correct.

Credit: https://commons.wikimedia.org/wiki/File:Moebiusband-1s.svg by user Ag2gaeh. License CC BY-SA 4.0.
