contractibility
the ability to contract
Contractibility is a property of a space in topology that measures the extent to which the space can be “contracted” into a smaller space. Specifically, a space is said to be contractible if it can be continuously deformed, via a homotopy, into a point.
Intuitively, this means that for a contractible space, we can take any point within the space, and shrink it down to a single point while continuously deforming the rest of the space so that its shape does not change.
The importance of contractibility in topology is that it is a sufficient condition for certain properties of a space. For example, a contractible space is simply-connected, which means that any loops in the space can be continuously deformed into a point. This is a helpful property when studying the fundamental groups of a space.
It is worth noting that not all spaces are contractible. For example, the torus (the surface of a donut) is not contractible, as there is a “hole” in the middle that cannot be shrunk down to a point.
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