anonymous
  • anonymous
here sir
Mathematics
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anonymous
  • anonymous
here sir
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
zzr0ck3r
  • zzr0ck3r
I dont understand the last sentence.
zzr0ck3r
  • zzr0ck3r
I know what Hausdorff is.

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anonymous
  • anonymous
A topological space is called a Hausdorff space, if for each x, y of distinct points of X, there exists U_{x} and U_{y} of x and y respectively that are disjoint. This implies X is Hausdorff with these properties except one.
zzr0ck3r
  • zzr0ck3r
It gives a definition of Hausdorff, and then said it implies something. There is no question here.
anonymous
  • anonymous
If \[\forall x, y \epsilon\mathbb X; x \neg y \]
zzr0ck3r
  • zzr0ck3r
that says the following: For all x and y in some space x, x is related to y.
zzr0ck3r
  • zzr0ck3r
Do you know what your question is?
anonymous
  • anonymous
\[There \exists U_x \epsilon N(x). U_y \epsilon N(y) \]
zzr0ck3r
  • zzr0ck3r
Are you listening to me?
anonymous
  • anonymous
\[U_x \bigcap U-y = \phi \]
zzr0ck3r
  • zzr0ck3r
ok man, I am gonna go then... this is pointless and a waste of time.
anonymous
  • anonymous
they said i should bring out the odd one
anonymous
  • anonymous
it is an option question
anonymous
  • anonymous
i am only trying to list all the options sir
anonymous
  • anonymous
zzr0ck3r
  • zzr0ck3r
for the 5th time, what is the question?
zzr0ck3r
  • zzr0ck3r
and please dont just retype what you already typed...
anonymous
  • anonymous
they defined the Hausdorff space and gave some properties , asking me to point out the odd property
zzr0ck3r
  • zzr0ck3r
do you mean \(U_x \bigcap U-\{y\} = \phi\) ?
zzr0ck3r
  • zzr0ck3r
or \(U_x \bigcap U_y-\{y\} = \phi\)
anonymous
  • anonymous
yes and i know that option A and B are properties of Hausdorff space but the C and D is where u am confused
anonymous
  • anonymous
the last option is \[\forall x, y \epsilon X, x \bigcap y = 0 \]
anonymous
  • anonymous
ok, i think option C is a typo error
zzr0ck3r
  • zzr0ck3r
Is there a reason you are not using parentheses when I keep asking you to?
anonymous
  • anonymous
may be they wanted to state\[ U_x \bigcap U_y = \phi \]
zzr0ck3r
  • zzr0ck3r
\(\forall x, y \epsilon\mathbb X; x \neg y\) makes no sense.
anonymous
  • anonymous
sir, i am so sorry about the parentheses but that was how the question came
zzr0ck3r
  • zzr0ck3r
But then you say yes when I say "should it be like this"
zzr0ck3r
  • zzr0ck3r
ok they all make sense except the equivalence one. \(\forall x, y \epsilon\mathbb X; x \neg y\)
zzr0ck3r
  • zzr0ck3r
I again, don't see how you are learning here. but what ever...
anonymous
  • anonymous
what about the last option. is it a property of Hausdorff space?
anonymous
  • anonymous
i mean this option \[∀x,yϵX,x⋂y=0 \]
zzr0ck3r
  • zzr0ck3r
sort of, it should say \(x\ne y\)
zzr0ck3r
  • zzr0ck3r
\(∀x,yϵX\text{ where } x\ne y, \{x\}⋂\{y\}=0\)
anonymous
  • anonymous
ok, so sorry again sir for the parenthesis , its because that the way it came . i am so sorry
anonymous
  • anonymous
A topological space X satisfies the first separation axiom T_{1 } if each one of any two points of X has a nbd that does not contain the other point. Thus,X is called a T_{1} - space otherwise known as what?
anonymous
  • anonymous
i think it is Hausdorff Space. am i correct ? @zzr0ck3r
zzr0ck3r
  • zzr0ck3r
no, it is not necessarily Hausdorff. I think they sometimes call \(T_1\) "accessible space". But I have never heard it referred to as anything but \(T_1\).

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