/sci/ - Science & Math

[Anonymous No.11637862]

I have the function

f:(R, T(a,b)) x (R, T[a,b)) -> (R, T[a,b)), f(x, y) = x,

where T(a,b) is the topology generated by the open intervals (a, b) and T[a,b) is generated by the half open intervals [a, b).

Is f continuous?

[Anonymous No.11637910]

Your function is not well defined and it makes no sense to ask about continuity unless you specify a topology (you need a topology on the topologies)

[Anonymous No.11637923]

>>11637910
I think he's writing the topological spaces more formally and using the implied product topology for the domain.
>>11637862
The function takes open sets to open sets, so yes, it is continuous.

[Anonymous No.11637934]

>>11637923
Oh. Then it's not continuous because the pre image of [0,1) is not open

[Anonymous No.11637939]

>>11637934
Oh, I don't understand topology well, clearly. I thought that you only consider the image of subsets in the domain, not the pre-images.

[Anonymous No.11637993]

>>11637939
What? A function is continuous if the preimage of every open set in the target is an open set in the domain. This is literally the second definition you learn.
Images are badly behaved.

[Anonymous No.11638014]

>>11637993
Yeah, I just had stuck in my head "takes open sets to open sets".
At least I won't make that error again.

[Anonymous No.11638556]

It's not open since for the inverse g of f and a an open set U in T[a, b) we have g(U) = U x R, which is not open since U is not open in T(a, b)

[Anonymous No.11638695]

Every single post above this is unironically, clinically retarded and has been written by a complete waste of air. That includes the OP.
I recommend slow, excruciating torture until death.
Retards.
Kill yourselves, retards.

[Anonymous No.11639012]

>>11638014
I made this mistake when I strated out with topology, dw OP.
The correct matra is "open sets are mapped from open sets" under a continuous function.