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I cant see the full question

describe the .....
It goes off the side of the page.

describe the set \[B _{0}( (0,0);1)

\(\{x\in \mathbb{R}^2 \mid \sqrt{x_1^2+x_2^2} <1\ \}\)

2) describe the open ball \[B _{0}( (0,0);1)\]

Er the inequality should read less than

word*

I'm on my phone and OpenStudy lags

Okay, it seems open balls of radius \(r\) centered at \(p\) are notated \(B_o(p;r)\)

so, what is the description?

yes, in general open is \(B(a,b)\) and closed is \(B[a,b]\)

you know my book did not explain that but this is just the question.

so, number the answers for me because it is two questions

ok . thank you sirs

show that the mapping f;R---.R+ defined by f(x)=e^x is homeomorphism

do you know what a homeomorphism is?

that is bijective funtiom f such that f and f^-1 are both continuous

it's bicontinuous, i.e. it's an invertible map that is continuous in both directions

its topological space question

any easy one will be ok

you need to tell us which one you are using, it's not a matter of one being easy or not :p

Cauchy definition

Which is?

For sure it is a bijection. Do you know how to prove that?

no

yes

so , that is the prove

Do you need to show they are continuous?

Or just go from the known fact that they both are?

just go from the known fact that they both are

Then you are done.

waw

what is waw? I see you make that comment before.

i mean you are a genius

not at all...

i wish i am good like you

1 year ago*

ok. got it . i have another quation

close this and ask a new one.

ok