Homotopic: Having the same (homo-) topological properties (-topic)
Comment on Baldur's Gayte
Zwiebel@feddit.org 1 week agoYou are talking about a straw of zero wall thickness right? A real straw should be homo-whatever to a torus
lennivelkant@discuss.tchncs.de 1 week ago
iAvicenna@lemmy.world 1 week ago
Even if it has thickness still homotopic to a circle. For instance a band with thickness is homotopic to a circle, you can retract along the radius to arrive at a circle that is inside the band. Similarly a plane, or a slab with thickness are all homotopic to a point.
Note that all of these are transformations are from the space to itself. So if you want to say something like “but you can also shrink a circle to eventually reach a point but it is not homotopic to a point” that won’t work because you are imagining transformation that maps a circle not into itself to a smaller one.
ps: the actual definition of homotopy equivalence between “objects” is slightly more involved but intuitively it boils down to this when you imagine one space as a subset of the other and try to see if they are homotopy equivalent.