Question

For the set A=(10,0)U(5,7)] intersect Q where Q is rational number
(i) find its interior points,
(ii) find its limit points,
(iii) determine if it is open or closed,
(iv) determine if it is compact,
(v) determine if it is connected.

Answer 1

is it(-10,0) maybe?

Answer 2

yes

Answer 3

and (5,7] instead of (5,7)] maybe?

Answer 4

[(-10,0) Union (5,7)] intersect with Q

Answer 5

ok
i think interior is empty
limit points: [(-10,0) Union (5,7)] intersect with Q union {-10,0,5,7}
not closed, becouse doesn't contain all limit points, not open becouse interior is empty
rest is easy

Answer 6

can i know why the interior point empty??

Answer 7

becouse every neighborhood of a rational point contains a irational nummbers. This means that there are no interior points in this set

Answer 8

the interior point is it written like this: [(-10,0) Union (5,7)] intersect with[Q union {-10,0,5,7}]??

Answer 9

first it's not interior, it's limit points. Second, it means the original set plus the -10,0,5,7

Answer 10

@mrs.love

Answer 11

@myko thanks..