Question

For the set A=[(-10,0)U(5,7)] intersect Q
(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

isnt there a theorem in rudin that says the union of two open sets is open?

Answer 2

can you find an open cover that covers that set? Can you then reduce that cover to a finite sub cover?

Answer 3

but how to find interior and limit point

Answer 4

aint open though is it?

Answer 5

last one is easiest, it is not connected because you have written it as the union of two disjoint sets

Answer 6

now that i look carefully, something is a bit wrong because no one writes an interval as (10,0)

Answer 7

maybe (-10,0)?

Answer 8

A=(10,0)U(5,7)
Yes, this part makes no sense for two reason. (10,0) is a backwards interval, and also... union of (0,10) and (5,7) would just be (0,10)

Satellite, it's probably what you said. (-10,0)
Kind of hilarious and surprising that even at this level of math we have people posting mangled problem statements...

Answer 9

no,i think set A=[(10,0]U(5,7)] intersect Q..