Let X be a topological space that satisfies the Kolmogorov axiom
(T0)
. Which of the following is not true about X?

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- anonymous

- katieb

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- anonymous

- anonymous

Any two different points of X have different closures
X contains no indiscrete subspace consisting of two points
X contains no indiscrete subspace consisting of more than one point
X has an indiscrete subspace consisting of two points only

- zzr0ck3r

what does it mean to be \(T_0\)?

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## More answers

- zzr0ck3r

in layman's terms

- anonymous

zeroth separation axiom

- zzr0ck3r

what does that mean?

- anonymous

if at least one of any two distinct points of a space has a
neighborhood that does not contain the other of these points

- anonymous

but i don't understand fully

- zzr0ck3r

which part?

- anonymous

because it looks like housdroff

- anonymous

contain the other of these points

- anonymous

i don't understand that statement

- anonymous

contain the other of these points

- zzr0ck3r

In hausdorff we have each element has a nbhd around it that does not intersect the other, this is a little less strong
We have a nhbd around one of them that does not contain the other.

- zzr0ck3r

I am going blowing with the fam, I will be back
Go read about T_0 spaces
Then remember closure means include boundary points, then make a statement about a set and its elements vs its boundary points

- anonymous

ok sir, i will read that

- anonymous

- anonymous

about the last question. i think D is the answer. am i correct?

- zzr0ck3r

why?

- zzr0ck3r

What they want here is for you to explain why each option is or is not correct.

- anonymous

but i read a page about the properties of that and D option was not among

- anonymous

so, which option is correct?

- anonymous

- anonymous

- zzr0ck3r

You are correct, I just wanted you do explain why.
Saying you went to a website, and saw the properties is not the best reasoning.

- anonymous

ok sir

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