2: Further Analysis of Subsets of R

Question 1

injection and surjection

Answer 1

bijection

Question 2

A is ___ if either A is empty of there is a ___ from natural numbers to A

Answer 2

countable/bijection

Question 3

The bijection from of countably infinite A is an ___

Answer 3

enumeration

Question 4

the set of ___ Q is ___

Answer 4

rationals/countable

Question 5

if f is ___ then the set of points where f is not ___ is countable

Answer 5

monotone/continuous

Question 6

the ___ numbers are uncountable

Answer 6

real

Question 7

Finite unions of closed sets are ___

Answer 7

closed

Question 8

Arbitrary intersections of closed sets are ___

Answer 8

closed

Question 9

the set of points from real numbers to real numbers is ___ in G-delta

Answer 9

continuous

Question 10

x is an ___ of E if x is a point of ___ of E{x}

Answer 10

accumulation point/closure

Question 11

a set E is perfect if it equals its set of ___

Answer 11

accumulation points

Question 12

the set of accumulatio points of E is ___

Answer 12

closed

Question 13

non-empty perfect sets are ___

Answer 13

uncountable

Question 14

the middle third Cantar set is ___,___,___, and equal to its set of ___

Answer 14

closes/non-empty/uncountable/accumulation points