Topology: Homeomorphisms

[@scottmoerschbacher8664]

Loving this series. Q: for your examples of homeomorphisms, the definition says we need a topology. Are you working in the standard topology? Continuity would depend on open intervals, etc., which would be dependent on the topology, as you’ve stated prior. Am I confused?? Many thanks,

[@mathprofessor-11235]

@scottmoerschbacher8664 thanks for watching! For the f(x)=3x example, i was using the standard topology on both and same thing for the tangent. Yes, continuity is dependent on the topologies, so a function could be continuous with respect to one topology and the same function could be not continuous with respect to another.

[@scottmoerschbacher8664]

@@mathprofessor-11235 amazing, many thanks for the quick reply ✌️