here sir

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- anonymous

here sir

- jamiebookeater

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- anonymous

- zzr0ck3r

I dont understand the last sentence.

- zzr0ck3r

I know what Hausdorff is.

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## More answers

- 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

It gives a definition of Hausdorff, and then said it implies something. There is no question here.

- anonymous

If \[\forall x, y \epsilon\mathbb X; x \neg y \]

- zzr0ck3r

that says the following:
For all x and y in some space x, x is related to y.

- zzr0ck3r

Do you know what your question is?

- anonymous

\[There \exists U_x \epsilon N(x). U_y \epsilon N(y) \]

- zzr0ck3r

Are you listening to me?

- anonymous

\[U_x \bigcap U-y = \phi \]

- zzr0ck3r

ok man, I am gonna go then... this is pointless and a waste of time.

- anonymous

they said i should bring out the odd one

- anonymous

it is an option question

- anonymous

i am only trying to list all the options sir

- anonymous

- zzr0ck3r

for the 5th time, what is the question?

- zzr0ck3r

and please dont just retype what you already typed...

- anonymous

they defined the Hausdorff space and gave some properties , asking me to point out the odd property

- zzr0ck3r

do you mean
\(U_x \bigcap U-\{y\} = \phi\)
?

- zzr0ck3r

or
\(U_x \bigcap U_y-\{y\} = \phi\)

- 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

the last option is \[\forall x, y \epsilon X, x \bigcap y = 0 \]

- anonymous

ok, i think option C is a typo error

- zzr0ck3r

Is there a reason you are not using parentheses when I keep asking you to?

- anonymous

may be they wanted to state\[ U_x \bigcap U_y = \phi \]

- zzr0ck3r

\(\forall x, y \epsilon\mathbb X; x \neg y\)
makes no sense.

- anonymous

sir, i am so sorry about the parentheses but that was how the question came

- zzr0ck3r

But then you say yes when I say "should it be like this"

- zzr0ck3r

ok they all make sense except the equivalence one.
\(\forall x, y \epsilon\mathbb X; x \neg y\)

- zzr0ck3r

I again, don't see how you are learning here. but what ever...

- anonymous

what about the last option. is it a property of Hausdorff space?

- anonymous

i mean this option \[∀x,yϵX,x⋂y=0 \]

- zzr0ck3r

sort of, it should say \(x\ne y\)

- zzr0ck3r

\(∀x,yϵX\text{ where } x\ne y, \{x\}⋂\{y\}=0\)

- anonymous

ok, so sorry again sir for the parenthesis , its because that the way it came . i am so sorry

- 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

i think it is Hausdorff Space. am i correct ? @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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