Real Analysis 1

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

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

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

{a} subset of R_d is open but not closed

[0,1] is an open subset of R_d

Union of an infinte number of closed sets is closed

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

(a,b) is a connected subset of R¹

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