Question

Topology in R^n!
Given J={(x,y):x^-y<=1}, the int J={x^2-y<1} and the J'=[x^2-y<=1}.
It's not-open, closed, and not-limited!
Can someone explain me why it is not limited, if it can't be more than 1?

Answer 1

anyone?

Answer 2

so u understand why its not open and closed ?

Answer 3

I know why it is not open but don't know why it is not closed. Please, explain

Answer 4

its closed :O

Answer 5

oh, it is not-open, closed. Mean it is not-open and it is closed. :)

Answer 6

ok, makes sense. How about not-limited?

Answer 7

j is closed since j' in topology

Answer 8

Not that, right? it is closed because \(J^c\) is open

Answer 9

well not really , sometimes a set is open and closed at the same time , also it might be not closed not open ( according to the definition )
yes exactly lol but see the question j' is j^c :)

Answer 10

and open means j in topology

Answer 11

How? in J', we have equal sign there --> it is not \(J^c\)

Answer 12

It is \(J^c \cup bd J\)

Answer 13

= Ext (J) , right?

Answer 14

ohh :O
yes right , sorry :P
ill the question dint specify things

Answer 15

However, I don't understand why int J = {x^2 -y <1} while J ={x^-1 y \(\leq 1\)}

Answer 16

I'm sorry for the delay on the reply. I was lunching.

the int of J is the set of point that belongs only to the interior of J.
or, as my professor explained
it's any element of J that, a "circle" centered on it,should only contain elements of J

Answer 17

I don't understand why J is not limited if it can't assume number less than 1.

Answer 18

whats the definition of limited and not limited /?

Answer 19

It's the existence of an upper or lower bond of the function?!?!

Answer 20

are u sure ?
im just asking wanna know if its the same in topology or not xD

Answer 21

not sure what you're going with this.....
please explain me like I never heard it before!
;)

Answer 22

hehe , im not sure of the definition of not limited in topology thats all :)

Answer 23

but, by your example, the function is limited.
couldn't take values minor than the function.

\[x^2 - y \le 1\]

Thus, is limited. It as a upper bound, right?

Answer 24

if we are talking about functions then yes its limited , but idk if its the same in topology

Answer 25

yes, we're talking about topology of functions in multivariable calculus.
This exercise is about the interior, the interior+border, open, closed, limited, etc. of subsets of \[R ^{2}\]