Here is the definition of CW-decomposition of a topological pair $(X,A)$ given in Tom Dieck's Algebraic topology textbook p.205
A sequence $A=X^{-1}\subset X^0\subset X^1 \subset ... \subset X^n$ is called a CW-decomposition of $(X,A)$ if it satisfies the followings:
(1) $X=\bigcup_{n\geq 0} X^n$
(2) $X^n$ is obtained from $X^{n-1}$ by attaching $n$-cells for $n\geq 0$
(3) $X$ carries the colimit topology with respect to the family $(X^n)$.
I don't understand the hypothesis (2) when it is $n=0$. What does it mean by attaching $0$-cells?
Attaching $0$-cells to $A$ is taking the disjoint union of $A$ and a discrete topological space, for example a single point. Here is $1$-dim cell complex I have shown before: Fig 4.17 from Topology and Groupoids.