Question

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

Answer 1

@zzr0ck3r

Answer 2

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

Answer 3

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

Answer 4

in layman's terms

Answer 5

zeroth separation axiom

Answer 6

what does that mean?

Answer 7

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

Answer 8

but i don't understand fully

Answer 9

which part?

Answer 10

because it looks like housdroff

Answer 11

contain the other of these points

Answer 12

i don't understand that statement

Answer 13

contain the other of these points

Answer 14

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.

Answer 15

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

Answer 16

ok sir, i will read that

Answer 17

@zzr0ck3r

Answer 18

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

Answer 19

why?

Answer 20

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

Answer 21

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

Answer 22

so, which option is correct?

Answer 23

@zzr0ck3r

Answer 24

@zzr0ck3r

Answer 25

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.

Answer 26

ok sir