anonymous
  • anonymous
Let X be a topological space that satisfies the Kolmogorov axiom (T0) . Which of the following is not true about X?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@zzr0ck3r
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
  • zzr0ck3r
what does it mean to be \(T_0\)?

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zzr0ck3r
  • zzr0ck3r
in layman's terms
anonymous
  • anonymous
zeroth separation axiom
zzr0ck3r
  • zzr0ck3r
what does that mean?
anonymous
  • 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
  • anonymous
but i don't understand fully
zzr0ck3r
  • zzr0ck3r
which part?
anonymous
  • anonymous
because it looks like housdroff
anonymous
  • anonymous
contain the other of these points
anonymous
  • anonymous
i don't understand that statement
anonymous
  • anonymous
contain the other of these points
zzr0ck3r
  • 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
  • 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
  • anonymous
ok sir, i will read that
anonymous
  • anonymous
@zzr0ck3r
anonymous
  • anonymous
about the last question. i think D is the answer. am i correct?
zzr0ck3r
  • zzr0ck3r
why?
zzr0ck3r
  • zzr0ck3r
What they want here is for you to explain why each option is or is not correct.
anonymous
  • anonymous
but i read a page about the properties of that and D option was not among
anonymous
  • anonymous
so, which option is correct?
anonymous
  • anonymous
@zzr0ck3r
anonymous
  • anonymous
@zzr0ck3r
zzr0ck3r
  • 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
  • anonymous
ok sir

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