As P.R. Halmos wrote, “the best notation is no notation.” If you can avoid introducing a new symbol, then the text is often more clear and the reader has one less thing to remember. A rule of thumb is to never use a letter only once. Consider the following definition:
A function $f$ is called a homeomorphism if it is continuous and has a continuous inverse.
The symbol $f$ serves no purpose since it is not used elsewhere in the definition. Thus, it can be omitted.