MCQ Bank
If \left( {X,\tau } \right) be a separable topology then it must have countable dense set.
- A) False
- B) True
- C)
- D)
Consider a set \(X\) with the indiscrete topology. What can be said about the singleton sets in \(X\)?
- A) They are closed but not open.
- B) They are open and closed.
- C) They are neither open nor closed.
- D) They are open but not closed.
A topological space is a \(T_{1}\)- space if and only if each of its finite subset is ....
- A) an open set
- B) neither open nor closed.
- C) both open and closed.
- D) a closed set.
Given a Hausdorff space (X, T) and a subset Y \subset X, with the subspace topology (Y, T_{Y}), which of the following statements is true?
- A) Y with the subspace topology (Y, T_{Y}) is not Hausdorff.
- B) Y must be connected.
- C) Y must be compact
- D) Y with the subspace topology (Y, T_{Y}) is also Hausdorff.
Given a Hausdorff space \((X, T)\) and a subset \(Y \subset X\), with the subspace topology \((Y, T_{Y})\), which of the following statements is true?
- A) Y must be connected.
- B) Y with the subspace topology \((Y, T_{Y})\) is not Hausdorff.
- C) Y must be compact
- D) Y with the subspace topology \((Y, T_{Y})\) is also Hausdorff.
Consider a set X with the indiscrete topology. What can be said about the singleton sets in X?
- A) They are closed but not open.
- B) They are neither open nor closed.
- C) They are open and closed.
- D) They are open but not closed.
A topological space is a T_{1}- space if and only if each of its finite subset is ....
- A) both open and closed.
- B) neither open nor closed.
- C) a closed set.
- D) an open set