Allen Hatcher's Algebraic Topology -- Unclear statement

95 Views Asked by At

In this definition (early on): enter image description here

He never specifies what $f_t | A = 1$ is supposed to mean in his preamble. What is $|$ being used for in this example?

1

There are 1 best solutions below

0
On

In "Standard Notations" on p. xii Hatcher writes

enter image description here : the identity function from a set to itself.

The vertical "$\mid$" is the standard notation for the restriction of a function. That is, $f_t\mid A$ denotes the restriction of $f_t : X \to X$ to the subspace $A \subset X$.