Real Analysis - II (Quiz 2)

• Homeomorphism

• not Homeomorphism

Say True or False:

Any discrete metric space M with more than one point is disconnected.

• true

• false

Say True or False :

R is not connected

• True

• False

A metric space M is said to be .................if every open cover for M has finite subcover.

• oscillation

• complete

• continuous

• compact

R with usual metric space is ...................

• not compact

• not connected

• countable

• compact

What is the definition of a connected

• M can be represented as the union of two disjoint open sets.

• A subset M where every point is an interior point.

• A subset M with no limit points.

• M cannot be represented as the union of two disjoint non-empty open sets.

Any Compact subsets of metric spaces M are

• open

• closed

• compact

• dense

A metric space M is .............. iff any family of closed sets with finite intersection property has non-empty intersection.

• complete

• connnected

• compact

• none of the above

• 1

• -1

• a

• 0

• True

• False