# Which surface is homeomorphism to mobius strip?

I'm a bit confused since I read many versions of this.

First of all, I couldn't understand how to define homeomorphism. Intuitively, I think that if I can deform an object, without tearing it, to another object, then those 2 surfaces are homeomorphic to each other. I definitely know the Mobius strip isn't homeomorphic to the torus since torus has 2 surfaces while Mobius strip has one.
I have also heard something about that if I could "map" the Mobius strip, then I could find the surface it is homeomorphic to.

Two topological spaces $(X_1,\tau_1)$ and $(X_2, \tau_2)$ are said to be homeomorphic provided that there exists a function $f: X_1 \rightarrow X_2$ such that $f$ is one-to-one, onto, continuous, and its inverse $f^{-1}$ is continuous. By continuous, we mean that the preimage of every open set in $X_2$ is open in $X_1$. What this means is that $X_1$ and $X_2$ have the same topological structure.
Visually, especially with spaces that are formed from the subspace topology of $\mathbb{R}^n$, this means that homeomorphisms are roughly the functions that are given by "stretching without tearing, pinching, or gluing," but the rigorous definition should be used for formal proofs.