R with usual metric {0} is


A) open

B) closed

C) half-open

D) none of these

Correct Answer:
B) closed

Description for Correct answer:
Any singleton set in R is closed.

Therefore {0} is closed.

Part of solved Real Analysis questions and answers : >> Elementary Mathematics >> Real Analysis








Comments

No comments available




Similar Questions
1). Which of the following is not true?
A). Q is not open in R
B). Z is not open in R
C). Any open interval (a, b) is o
D). [0, 1) is open in R
-- View Answer
2). Let M be any non-empty set Define \[d(x,y)=\begin{cases}0\text{ if }x=y\\1\text{ if }x\ne y\end{cases}\] This metric is called
A). Stanaard Metric
B). Discrete Metric
C). Absolute Metric
D). Bounded Metric
-- View Answer
3). Which of the following is not correct?
A). In a discrete metric space every-subset is open
B). \(\phi\) is open 3
C). Union of any family of open set is open
D). Arbitrary intersection of ope'nI sets is open
-- View Answer
4). Let R be a metric space with usual metric \(\Large A_{n}= \left(\frac{-1}{n},\frac{1}{n}\right) \). Then \(\Large\bigcap\limits_{n=1}^{\infty}A_{n}\) is
A). open
B). not open
C). not singleton set
D). \(\phi\)
-- View Answer
5). Let (M, d) be a metric space. Let \(x\in M\). Then \(\{x\}^{c}\) is
A). open
B). closed
C). not open
D). half-open
-- View Answer


6). Any open subset of R can be expressed as the union of a countable number of
A). closed sets
B). mutually disjoint closed sets
C). open sets
D). mutually disjoint open intervals
-- View Answer
7). Every convergent sequence is a
A). cauchy sequence
B). optimal sequence
C). increasing sequence
D). decreasing sequence
-- View Answer
8). Every cauchy sequence is convergent. The statement is
A). true
B). false
C). partially true
D). none of these
-- View Answer
9). Every contmuousimage of a connected set is
A). connected
B). disconnected
C). compact
D). none of these
-- View Answer
10). If f is diffrentiable at c. Then f is
A). Monotonic
B). Discontinuous
C). Continuous
D). None of these
-- View Answer