Question

1)
the internsection of infinite number of opens need not be open in general (i) The intersection of an finite number of open sets is open. which is right​

Answer 1

Answer:

Step-by-step explanation:More specifically, let O1,...,On be a finite collection of open subsets of the continuum, C. Then the intersection O1∩⋅⋅⋅∩On is open as well. I think it is possible to do it without considering metric spaces (and therefore balls of radius r). Also, if you could prove why the intersect of an infinite amount of open subsets turns out to be possibly closed, it would be very much appreciated as this is difficult to wrap my head around.

Also open sets are defined as sets that don't contain their endpoints. Sorry for being unclear.