1 votes 1 votes Let $X$ be a non-empty topological space such that every function $f : X \rightarrow \mathbb{R}$ is continuous. Then $X$ has the discrete topology $X$ has the indiscrete topology $X$ is compact $X$ is not connected Linear Algebra tifrmaths2014 vector-space + – makhdoom ghaya asked Dec 17, 2015 • edited Aug 17, 2020 by soujanyareddy13 makhdoom ghaya 305 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.