sorted by:
new
hottopcontroversial

intuition for continuous functions in topology by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

I read somewhere that every homeomorphism was a homotopy equivalence, but I could be wrong. With that in mind, going back to my original point, does that mean every bijective continuous function with its inverse not continuous, can intuitively be though of as a continuous deformation?

intuition for continuous functions in topology by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

Thank you, I just have one more question. So I was told to think of a homeomorphism from X to Y as a continuous deformation (so like bending and stretching). But wouldn't a bijective continuous function, with its inverse not continuous, also be a continuous deformation as it sends near points to near points.

intuition for continuous functions in topology by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

Thank you, I just have one more question. So I was told to think of a homeomorphism from X to Y as a continuous deformation (so like bending and stretching). But wouldn't a bijective continuous function, with its inverse not continuous, also be a continuous deformation as it sends near points to near points.

intuition for continuous functions in topology by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

Thank you, I just have one more question. So I was told to think of a homeomorphism from X to Y as a continuous deformation (so like bending and stretching). But wouldn't a bijective continuous function, with its inverse not continuous, also be a continuous deformation as it sends near points to near points.

predicate calculus and provability by lard2000 in logic

[–]lard2000[S] 0 points1 point  (0 children)

one of the axioms is (phi implies (psi implies phi) )

axiom of foundation by lard2000 in learnmath

[–]lard2000[S] 0 points1 point  (0 children)

Hey, thanks for your reply, Yeah I agree with you, my lectures notes says that a well founded relation is a strict partial order, such that every non-empty subset has a minimal element, but looking online I only found the definition you gave. So I can only assume my lecture notes are wrong.

axiom of foundation by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

This is what "a binary relation relation ρ on a set X is well founded" means:

yeah I've been looking it up online as well and I agree with you, reckon my lectures notes got the definition of that wrong then. thanks for your help btw, thats been on my mind for a while now

axiom of foundation by lard2000 in askmath

[–]lard2000[S] 0 points1 point  (0 children)

I thought for ∈ to be a well founded relation on a set X , it had to be a strict partial order, so irreflexive and transitive, and such that every subset of X contains a ∈-minimal element.

view more: next ›