[Tex/LaTex] How to typeset a small black square as a binary operator

Question

This is my first post on this SE so I apologize if my formatting is bad.

Essentially I am trying to reproduce the small black symbol from the following definition in Allen Hatcher's Algebraic Topology:

(This book can also be accessed from his website for free, and this particular image is from page 26.)

I am trying to figure out how to typeset the small black square between the f and the g(s). I tried the following in my preamble

\renewcommand{\bullet}{\tiny$\blacksquare$}

but the square bullet produced looks jarring and does not look like a binary operator, i.e. it is not centered and does not have equal spacing between f and g(s).

Would any of you have any suggestions on how to make this particular symbol?

Answer 1

This is actually not a square but just the shape of \cdot from the Lucida family used in the picture.

\documentclass{article}
\usepackage{lucidabr}
\begin{document}
$f \cdot g$
\end{document}

Lucida is a commercial font, you can purchase it from TUG.

---

You could also go ahead and fake the symbol using a \rule.

\documentclass{article}
\renewcommand\bullet{%
  \mathbin{\mskip1mu
    \mathchoice
      {\squarebullet{.25ex}{.25ex}}%
      {\squarebullet{.25ex}{.25ex}}%
      {\squarebullet{.18ex}{.18ex}}%
      {\squarebullet{.15ex}{.15ex}}
    \mskip1mu}
}
\newcommand\squarebullet[2]{\vcenter{\hbox{\rule{#1}{#2}}}}
\begin{document}
$f \cdot g_{f \cdot g_{f \cdot g}}$

$f \bullet g_{f \bullet g_{f \bullet g}}$
\end{document}