मान लीजिए कि (X, d) एक मीट्रिक समष्टि है। यदि X पूर्ण (complete) और पूर्णतः परिबद्ध (totally bounded) है, तो X क्या है?

Which of the following statements is true for any metric space X?

Which of the following defines a metric on ℝ?

Let (X, d) be a metric space. Which of the following statements are true? 1. Every compact subset of (X, d) is closed and bounded. 2. Every closed and bounded subset of (X, d) is compact. 3. Every compact subset of (X, d) is open. 4. Any finite subset of (X, d) is compact.