Sorry, did not make the notion of deformation precise. The idea is that stretching and compressing cannot include attaching one part to another, or tearing it.  The mathematical term is that of a "homeomorphism" , which is a one to one, onto, and continuous map. The precise statement is that the figure 8 is not homeomorphic to zero.  A good place to look is 

https://www.google.com/books/edition/Basic_Topology/NJbuBwAAQBAJ?hl=en&gbpv=1&printsec=frontcover