Register

TIFR-2016-Maths-B: 21

• edited by
200 views
0 votes
0 votes

Let $A_{1}\supset A_{2}\supset \cdots \supset A_{n}\supset A_{n+1}\supset \cdots$  be an infinite sequence of non-empty subsets of  $\mathbb{R}^{3}$. which of the following conditions ensures that their intersection is non-empty ?

  1. Each $A_{i}$ is uncountable
  2. Each $A_{i}$ is open
  3. Each $A_{i}$ is connected
  4. Each $A_{i}$ is compact.
• edited by
User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

0 votes
0 votes
0 answers
1
soujanyareddy13 asked Aug 30, 2020
164 views
TIFR-2016-Maths-B: 22
Let $(X,d)$ be a metric space. Which of the following is possible ? $X$ has exactly $3$ dense subsets $X$ has exactly $4$ dense subsets $X$ has exactly $5$ dense subsets $X$ has exactly $6$ dense subsets.
Let $(X,d)$ be a metric space. Which of the following is possible ? $X$ has exactly $3$ dense subsets$X$ has exactly $4$ dense subsets$X$ has exactly $5$ dense subsets$X$...
User Avatar
0 votes
0 votes
0 answers
2
soujanyareddy13 asked Aug 30, 2020
138 views
TIFR-2016-Maths-B: 23
Let $\left \{ f_{n} \right \}^{\infty }_{n=1}$ be the sequence of functions on $\mathbb{R}$ defined by $f_{n}\left ( x \right )=n^{2}x^{n}.$. Let $A$ be the set of all points $a$ in $\mathbb{R}$ ... $A=\left \{0\right \}$ $A=\left [0,1\right )$ $A=\mathbb{R}\setminus \left \{-1,1\right \}$ $A=\left (-1,1\right ).$
Let $\left \{ f_{n} \right \}^{\infty }_{n=1}$ be the sequence of functions on $\mathbb{R}$ defined by $f_{n}\left ( x \right )=n^{2}x^{n}.$. Let $A$ be the set of all po...
User Avatar
0 votes
0 votes
0 answers
3
soujanyareddy13 asked Aug 30, 2020
163 views
TIFR-2016-Maths-B: 24
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a continuous function such that $f\left ( i \right )=0$, for all $i \in \mathbb{Z}$. Which of the following statements is always true ? Image $(f)$ is closed in $\mathbb{R}$ Image $(f)$ is open in $\mathbb{R}$ $f$ is uniformly continuous None of the above.
Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a continuous function such that $f\left ( i \right )=0$, for all $i \in \mathbb{Z}$. Which of the following statements is alwa...
User Avatar
Link Copied!