Question

here sir

Answer 1

@zzr0ck3r

Answer 2

I dont understand the last sentence.

Answer 3

I know what Hausdorff is.

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

that says the following:

For all x and y in some space x, x is related to y.

Answer 8

Do you know what your question is?

Answer 9

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

Answer 10

Are you listening to me?

Answer 11

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

Answer 12

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

Answer 13

they said i should bring out the odd one

Answer 14

it is an option question

Answer 15

i am only trying to list all the options sir

Answer 16

@zzr0ck3r

Answer 17

for the 5th time, what is the question?

Answer 18

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

Answer 19

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

Answer 20

do you mean

\(U_x \bigcap U-\{y\} = \phi\)

?

Answer 21

or

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

Answer 22

yes and i know that option A and B are properties of Hausdorff space but the C and D is where u am confused

Answer 23

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

Answer 24

ok, i think option C is a typo error

Answer 25

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

Answer 26

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

Answer 27

\(\forall x, y \epsilon\mathbb X; x \neg y\)

makes no sense.

Answer 28

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

Answer 29

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

Answer 30

ok they all make sense except the equivalence one.

\(\forall x, y \epsilon\mathbb X; x \neg y\)

Answer 31

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

Answer 32

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

Answer 33

i mean this option \[∀x,yϵX,x⋂y=0 \]

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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?

Answer 38

i think it is Hausdorff Space. am i correct ? @zzr0ck3r

Answer 39

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 \(T_1\).