TIFR-2014-Maths-B-8

Question

Let $X$ be a non-empty topological space such that every function $f : X \rightarrow \mathbb{R}$ is continuous. Then 

• A. $X$ has the discrete topology 
• B. $X$ has the indiscrete topology 
• C. $X$ is compact 
• D. $X$ is not connected