Comment on Baldur's Gayte

iAvicenna@lemmy.world ⁨6⁩ ⁨days⁩ ago

• Zwiebel@feddit.org ⁨6⁩ ⁨days⁩ ago

  You are talking about a straw of zero wall thickness right? A real straw should be homo-whatever to a torus

  source

  • iAvicenna@lemmy.world ⁨5⁩ ⁨days⁩ 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.

    source
  • lennivelkant@discuss.tchncs.de ⁨6⁩ ⁨days⁩ ago

    Homotopic: Having the same (homo-) topological properties (-topic)

    source
• stevedice@sh.itjust.works ⁨4⁩ ⁨days⁩ ago

  I think people don’t know a torus is hollow.

  source
• ytg@sopuli.xyz ⁨6⁩ ⁨days⁩ ago

  Wouldn’t a straw be the product of a circle and a line?

  source

  • iAvicenna@lemmy.world ⁨5⁩ ⁨days⁩ ago

    What you said is stronger than being homotopic. homotopic is weaker, for instance a line is homotopic to a point, By taking the straw (even if it has thickness) and just shrinking it along its longer axis you eventually arrive at a circle. If it has thickness you will arrive at a band and then you can also retract radially to arrive at a circle.

    source
• Semjaza@lemmynsfw.com ⁨6⁩ ⁨days⁩ ago

  A CD is clearly homotopic to a torus, though…

  And the walls of a straw do have thickness…
  A straw goes:

  Gas - solid - gas - solid - gas

  source

  • iAvicenna@lemmy.world ⁨5⁩ ⁨days⁩ ago

    If solid torus yes, if just the regular torus (surface of the solid torus) no. CD is homotopic to a circle and so is a solid torus.

    source

    • Semjaza@lemmynsfw.com ⁨5⁩ ⁨days⁩ ago

      OK, that’s my ignorance. I didn’t realise toruses were usually hollow.

      Thank you for letting me know, you’re right and I’ve learnt something.

      source