Real Analysis 1

The open interval (0, 1) can be expressed as a union of closed sets.

(a)  

In any Metric space M, empty sets are both open and closed

(a)  

Intersection of infinite number of open sets in a metric space is always open

(a)  

{a} subset of R_d is open but not closed

(a)  

[0,1] is an open subset of R_d

(a)  

Union of an infinte number of closed sets is closed

(a)  

If f is a homeomorphism from M₁ to M₂, then f^-1 is continous.

(a)  

(a,b) is a connected subset of R¹

(a)  

If M is connected then every characteristic function on M is Constant

(a)