Real Analysis II

A metric space S is called ______ if S=AUB where A and B are disjoint nonempty open sets in S.

• disconnected

• connected

• closed

• open

Every open interval in R is_______.

• connected

• disconnected

• closed

• half-open

The set Q of rational numbers is ____________________

• connected

• disconnected

• closed

• half-open

If a continuous function f takes two values 0 and 1 then f is called a ____ valued function.

• single

• multiple

• two

• triple

The continuous image of a connected set is ________

• connected

• disconnected

• constant

• unity

One of the simplest step function is the  ________________ function.

•  continuous 

• composite 

• greatest integer

•  discontinuous

Every convex set is _____  connected

• arcwise

• linewise

• segment

• continuously

Let f be defined on [a,b] and c is an interior point in [a,b]. Then f(c ) - f(c- ) is called the ___ jump of f at c

• righthand

• lefthand

• central

• finite

If f is differentiable at c, then f is _____ at c.

• constant

• discontinuous

• continuous

• connected

If f is monotonic on [a,b] then the set of discontinuities of f is _____

• countable

• uncountable

• infinite

• zero