Topological Characterization of Continuity

[felvt]

Let g be defined on all of R. If A is a subset of R, define the set g^-1 (A) by

g^-1 (A)={x belong to R:g(x) belong to A}.

show that g is continous if and only if g^-1 (O) is open whenever O being a subset R is an open set.

 

[pka]

I would be glad to give you a solution. However on the site using absolute value signs crashes the TeX. You might call the problem to the administrators attention.

 

[felvt]

Don't really see what you are talking about, but ok. |

 

[daon]

I would be glad to give you a solution. However on the site using absolute value signs crashes the TeX. You might call the problem to the administrators attention.

pka, using "\mid" will work fine.

 

[pka]

I would be glad to give you a solution. However on the site using absolute value signs crashes the TeX. You might call the problem to the administrators attention.

pka, using "\mid" will work fine.

What does that mean?
What is \mid? It is not necessary at any other site. Why this one?

 

[daon]

I have also noticed the problem with the absolute values. One or two sometimes worked for me, but when using several |'s, it would crash as you said. "\mid" is the only work-around I found that works 100% of the time...

\(\displaystyle \mid x-c \mid < \delta \Rightarrow \mid f(x)-f(c) \mid < \epsilon\)

\mid x-c \mid < \delta \Rightarrow \mid f(x)-f(c) \mid < \epsilon