MathOverflow

I am not an expert in asymptotics of orthogonal polynomials, so I would appreciate verification from people who know this area.
I was reading the paper
C. Féliz-Sánchez, H. Pijeira-Cabrera, J. Quintero-Roba, Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis, Mathematics 12 (2024), 1082....

Disclaimer: I'm not at all a specialist of optimal transportation.
After struggling a bit with metrising a space of objects I'm working with (which I do not give any details about, as it is a completely unrelated field and I'd have to introduce looots of things), turned out the definition I was looking for was the Bottleneck...

Let $X$ to be a connected, compact CW complex.
It is called an $H$-space, if there is a point $e\in X$ and a continuous map $\mu\colon X \times X \to X$, such that $\mu(x,e)=\mu(e,x)=x$ for all $x\in X$.
It admits a Maltsev operation, if there is a continuous map $m\colon X \times X \times X \to X$, such that $m(x,y,y)=m(y,y,x)=x$ for all $x,y\in X$....

In what follows, all vector spaces are over the field of scalars $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$. One has as basic facts in functional analysis that:
Any bounded linear operator $T:E\rightarrow F$ between normed vector spaces $E,F$ (i.e. $T(K)\subset F$ is bounded whenever $K\subset E$ is bounded) is continuous;...