What does the notation $xf$ mean in the context of a map $f: X \rightarrow Y$. I am reading an older textbook on Homology Theory (P.J. Hilton & S. Wylie "Homology Theory: An Introduction to Algebraic Topology") and came across a notation that I am not familiar with used throughout the book.
The notation is relating to a mapping $f: X \rightarrow Y$ which is $xf$ for some $x \in X$. Does anyone know what this means? The first time it is used is in the following paraphrased paragraph:
"A map $f: X \rightarrow Y$ from the space $X$ to the space $Y$ is a continuous function from $X$ to $Y$. ... If $X_0 \subseteq X$, then $X_0f$ is the set of points $xf$, $x \in X_0$, and is called the f-image of $X_0$."
 A: I presume you are familiar with ordinary prefix notation $f(x)$ for function values.
This is simply postfix notation: instead of the usual prefix notation $f(x)$ where the function symbol comes before the argument (with parentheses around the argument), in postfix notation $x f$ the function symbol comes after the argument (without any parentheses).
So, if you prefer, you can read this by simply replacing postfix notation with prefix notation.
A: Some authors do not use the symbol $f(x)$ to denote the image of $x \in X$ under $f$, but write $xf$ for it. This is just a notational issue, and one does not see it often.
However  it has a benefit. If we have functions $f:X \to Y$ and $g:Y \to Z$, we usually define their composition $g \circ f:X \to Z$ by $(g \circ f)(x) = g(f(x))$. But in a sense this convention reverses the order: We use to read from left to right, thus $g \circ f$ seems to indicate that we start with $g$ and take $f$ after it - although it is just the other way.
In the other functional notation we write $f \circ g : X \to Z, x(f \circ g) = xfg$.
