You are Here: Home >< Maths

# topomagikal spaces watch

1. so we're working in the topology of pointwise convergence over functions f:[0,1]->real.

f_n=1-nx for
0 otherwise.

wat is the interior, boundary and closure of the set {f_n|neN}

we think that the interior is the empty set but are unsure about the boundary and closure.
2. srsly.

(Original post by DFranklin)
x
3. What are your definitions of interior, boundary and closure?
4. (Original post by DFranklin)
What are your definitions of interior, boundary and closure?
they'd be equivalent to whatever you're thinking of.

interior of H is the largest open subset of H
closure of H is the smallest closed superset of H
boundary of H is the set of points such that any open set containing the point contains a point inside H and a point in T\H
5. I messed that one up on the test. Didn't realise till a few hours later.
For the closure I think that it's the whole of F[0,1], since a finite (or even countable) intersection of the sub-basis sets will have some function that goes through every 'window' at x, i.e. , and you can make that function take values when
Hence for every function in F[0,1], any open set including the function will include one that intersects A.

Then if the interior is empty (I think it is too) the boundary is just .
6. (Original post by benwellsday)
I messed that one up on the test. Didn't realise till a few hours later.
For the closure I think that it's the whole of F[0,1], since a finite (or even countable) intersection of the sub-basis sets will have some function that goes through every 'window' at x, i.e. , and you can make that function take values when
Hence for every function in F[0,1], any open set including the function will include one that intersects A.

Then if the interior is empty (I think it is too) the boundary is just .
Good work BWD.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 13, 2010
Today on TSR

### University open days

1. University of Cambridge
Wed, 26 Sep '18
2. Norwich University of the Arts
Fri, 28 Sep '18
3. Edge Hill University
Faculty of Health and Social Care Undergraduate
Sat, 29 Sep '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams