I'm taking a course that uses the book "algebraic topology" by Allen Hatcher. In this book there are two different ways in which a pair $(X,A)$ of a topological space $X$ and a subspace $A$ can be nice: They can have the "homotopy extension property" (HEP) and they can be a "good pair". The definition of HEP can be found on Wikipedia, and we say that $(X,A)$ is a good pair if $A$ is closed and non-empty and is a deformation retract of a neightborhood in $X$.
Are there examples of good pairs that does not have the HEP? And are there pairs that have the HEP without being good pair? Are they equivalent under some assumption (e.g. $X$ being $\mathbb{R}^n$?)