/sci/ - Science & Math

>>11189838
Let A and B be homeomorphic. If I delete a point x of A, I can delete a point y of B such that A\{x} is homeomorphic to B\{y}.
Corollary: Let A and B be homeomorphic. If I delete a point x of A, I can delete a point y of B such that A\{x} and B\{y} have the same number of connected components.

Example of application of corollary: Delete a point on the unit circle. The result is homeomorphic to the open unit interval and connected. Deleting any point on the line makes it stop being connected, so the line and the circle aren't homeomorphic.

>>10717755
>But instead of shooting the targets, you are now shooting yourself.
Extremely accurate.
>>10716235
Remind me, was there a 0 A.D. or a 0 B.C.?

>>10405563
Algebraic topology already has applications to physics.

For whoever requested it