Register

TIFR-2015-Maths-B-11

350 views
1 votes
1 votes

Let $(X, d)$ be a path connected metric space with at least two elements, and let $S=\left\{d(x, y):x, y \in X\right\}$. Which of the following statements is not necessarily true ?

  1. $S$ is infinite.
  2. $S$ contains a non-zero rational number.
  3. $S$ is connected.
  4. $S$ is a closed subset of $\mathbb{R}$
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

1 votes
1 votes
0 answers
1
makhdoom ghaya asked Dec 20, 2015
333 views
TIFR-2015-Maths-B-4
Let $U_{1}\supset U_{2} \supset...$ be a decreasing sequence of open sets in Euclidean $3$-space $\mathbb{R}^{3}$. What can we say about the set $\cap U_{i}$ ? It is infinite. It is open. It is non-empty. None of the above.
Let $U_{1}\supset U_{2} \supset...$ be a decreasing sequence of open sets in Euclidean $3$-space $\mathbb{R}^{3}$. What can we say about the set $\cap U_{i}$ ?It is infin...
User Avatar
2 votes
2 votes
0 answers
2
makhdoom ghaya asked Dec 21, 2015
449 views
TIFR-2015-Maths-B-15
Let $d(x, y)$ be the usual Euclidean metric on $\mathbb{R}^{2}$. Which of the following metric spaces is complete? $\mathbb{Q}^{2}\subset\mathbb{R}^{2}$ with the metric $d(x, y)$. $[0, 1]\times [0, \infty)\subset \mathbb{R}^{2}$ ... $d''(x, y) = \min \left \{ 1, d(x, y) \right \}$.
Let $d(x, y)$ be the usual Euclidean metric on $\mathbb{R}^{2}$. Which of the following metric spaces is complete?$\mathbb{Q}^{2}\subset\mathbb{R}^{2}$ with the metric $d...
User Avatar
5 votes
5 votes
2 answers
4
makhdoom ghaya asked Dec 20, 2015
957 views
TIFR-2015-Maths-B-5
Let $n \geq 1$ and let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$, for some $k \geq 1$. Let $I$ be the identity $n \times n$ matrix. Then. $I+A$ need not be invertible. Det $(I+A)$ can be any non-zero real number. Det $(I+A) = 1$ $A^{n}$ is a non-zero matrix.
Let $n \geq 1$ and let $A$ be an $n \times n$ matrix with real entries such that $A^{k}=0$, for some $k \geq 1$. Let $I$ be the identity $n \times n$ matrix. Then.$I+A$ n...
User Avatar
Link Copied!