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i think frechet space

correct

chill, reading

1) and 3) are true, I cant tell what you mean by the last line

\[Iff for x, y \epsilon X x\epsilon U_{x}and y\epsilon U_{y} \] the last statement

\[\forall x,y\in X \ x\in U_x\text{ and } y\in U_y\]
What are \(U_x, U_y\) ?

It has to be the open one.

What open sets?

\[\epsilon \neq \in\]

Don't une `\epsilon` to mean "in" :)

Ux and Uy are open sets not given the open sets sir .
ok. what about option 2. is it right?

thanks for tell me that sir

2) is not true

unless it is finite.

lol

homeomorphism

homomorphism is a group concept

sorry C

correct

sorry wrong option sir

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

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

c
\[ \forall x, y \epsilon X, x \bigcap y = 0 \]

what is \(\neg\)?

i think they want to confuse me with that or its an error

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

to me C is true

B is also true

but a and d, i am confuse

ok sir, what if option A was
\[If \forall x, y \epsilon\mathbb X; x \rightarrow y \] is it correct?

can you take a screen shot?

you latex work needs some love :)

lol

i will but its not always clear

or put the text in `\text{stuff here}`
Example
\(\text{if }x\in X\text{ then } \forall x\)

ok close this and ask a new one if you have something else.

tag me if you need me...

There exists U_x \epsilon N(x). U_y \epsilon N(y) here is how option B is

is epsilon not same as in?

nope. epsilon is a greek letter, in is just means ... in :)

That option makes no sense...

it din't show fully but thats how it is.ok. thank you sir

or it is trivially true.
can you say in normal words what that option says?

hmmm

Are you on windows?

but, so, that option is wrong since a set containing X can not be in the neighborhood of x

no sir.

Why cant a set containing \(x\) not be in \(N(x)\)?

\(N(x)\subseteq N(x)\).
Unless you mean \(\in\) in which case it is weird....

N(x) means elements around X and not sets around X. i might be wrong

ok. can we try another?

close this please, it takes to long to scroll on this pc