## anonymous one year ago here sir

1. anonymous

@zzr0ck3r

2. zzr0ck3r

I dont understand the last sentence.

3. zzr0ck3r

I know what Hausdorff is.

4. 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.

5. zzr0ck3r

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

6. anonymous

If $\forall x, y \epsilon\mathbb X; x \neg y$

7. zzr0ck3r

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

8. zzr0ck3r

Do you know what your question is?

9. anonymous

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

10. zzr0ck3r

Are you listening to me?

11. anonymous

$U_x \bigcap U-y = \phi$

12. zzr0ck3r

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

13. anonymous

they said i should bring out the odd one

14. anonymous

it is an option question

15. anonymous

i am only trying to list all the options sir

16. anonymous

@zzr0ck3r

17. zzr0ck3r

for the 5th time, what is the question?

18. zzr0ck3r

19. anonymous

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

20. zzr0ck3r

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

21. zzr0ck3r

or $$U_x \bigcap U_y-\{y\} = \phi$$

22. 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

23. anonymous

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

24. anonymous

ok, i think option C is a typo error

25. zzr0ck3r

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

26. anonymous

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

27. zzr0ck3r

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

28. anonymous

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

29. zzr0ck3r

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

30. zzr0ck3r

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

31. zzr0ck3r

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

32. anonymous

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

33. anonymous

i mean this option $∀x,yϵX,x⋂y=0$

34. zzr0ck3r

sort of, it should say $$x\ne y$$

35. zzr0ck3r

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

36. anonymous

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

37. 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?

38. anonymous

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

39. 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 $$T_1$$.