![general topology - Let $X$ be a topological space, and $f,g: X \to \mathbb{R}$ be continuous functions. Then show (1) and (2). - Mathematics Stack Exchange general topology - Let $X$ be a topological space, and $f,g: X \to \mathbb{R}$ be continuous functions. Then show (1) and (2). - Mathematics Stack Exchange](https://i.stack.imgur.com/1RZPU.jpg)
general topology - Let $X$ be a topological space, and $f,g: X \to \mathbb{R}$ be continuous functions. Then show (1) and (2). - Mathematics Stack Exchange
![general topology - A function between topological spaces is an open, continuous bijection if and only if it is a homeomorphism. - Mathematics Stack Exchange general topology - A function between topological spaces is an open, continuous bijection if and only if it is a homeomorphism. - Mathematics Stack Exchange](https://i.stack.imgur.com/dDuJT.png)
general topology - A function between topological spaces is an open, continuous bijection if and only if it is a homeomorphism. - Mathematics Stack Exchange
mathsub.com on X: "The topological definition of a continuous function involves preimages of open and closed sets. #MathGRE #Analysis #Topology https://t.co/mqheb4R2kS" / X
![general topology - Continuous functions in topological spaces and neighborhoods - Mathematics Stack Exchange general topology - Continuous functions in topological spaces and neighborhoods - Mathematics Stack Exchange](https://i.stack.imgur.com/lBM6N.png)