List of top Mathematics Questions on Topology asked in IIT JAM MA

Consider the intervals \( S = (0, 2] \) and \( T = [1, 3] \). Let \( S^\circ \) and \( T^\circ \) be the sets of interior points of \( S \) and \( T \), respectively. Then the set of interior points of \( S \setminus T \) is equal to

The set \[ \left\{ \frac{x}{1+x^2} : -1<x<1 \right\}, \text{ as a subset of } \mathbb{R}, \text{ is} \]

The set \[ \left\{ \frac{1}{m} + \frac{1}{n} : m, n \in \mathbb{N} \right\} \cup \{0\}, \text{ as a subset of } \mathbb{R}, \text{ is} \]