mjhjmtu

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

renewcommandbullettiny$blacksquare$

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?

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

documentclassarticle
usepackagelucidabr
begindocument
$f cdot g$
enddocument

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

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

documentclassarticle
renewcommandbullet%
 mathbinmskip1mu
 mathchoice
 squarebullet.25ex.25ex%
 squarebullet.25ex.25ex%
 squarebullet.18ex.18ex%
 squarebullet.15ex.15ex
 mskip1mu

newcommandsquarebullet[2]vcenterhboxrule#1#2
begindocument
$f cdot g_f cdot g_f cdot g$

$f bullet g_f bullet g_f bullet g$
enddocument

This symbol exists in the mathabx font package. Here is a way to use this symbol without having to load the package:

documentclassarticle
DeclareFontFamilyUmathbhyphencharfont45
DeclareFontShapeUmathbmn%
<-6> mathb5 %
 <6-7> mathb6
 <7-8> mathb7 %
 <8-9> mathb8 %
 <9-10> mathb9 %
 <10-12> mathb10 %
 <12-> mathb12 %
 
DeclareSymbolFontmathbUmathbmn
DeclareMathSymbolsqbulletmathbinmathb"0D

begindocument

[ f sqbullet g]%

enddocument 

Decide for the size of the black dot, here it is twice the size of (the bounding box of) a period, with a small sidebearing.

documentclassarticle
usepackageamsmath

makeatletter
newcommandpp% check it's not defined
DeclareRobustCommandppmathbinmathpalettepp@relax
newcommandpp@[2]%
 mspace0.5mu%
 vcenterhboxsboxz@$#1.$rule2htz@2htz@%
 mspace0.5mu%

makeatother

begindocument

$fpp g$

$scriptstyle fpp g$

enddocument

I don't know the exact size of the black square as in the picture of the OP. I have made this with a new command bsq:

documentclass[12pt]article
usepackageamssymb,amsmath
usepackagescalerel
newcommandbsqmkern 5mublacksquaremkern 9mu

begindocument
[fraisebox1ptscaletobsq2pt g(s)=
begincases
f(2s) &\
g(2s-1)&
endcases]

enddocument

This glyph is available in several packages as smblksquare, including unicode-math (which I recommend), stix and stix2. Its Unicode codepoint is ▪ (U+25AA). Just define an operator with spacing mathbin.

documentclass[varwidth]standalone
usepackageunicode-math

newcommandcsquaremathbinsmblksquare

begindocument
( f csquare g )
enddocument

There are several similar symbols, such as vysmblksquare for a smaller version (⬝) or mdlblksquare for a larger one (◼). For example:

documentclass[varwidth]standalone
usepackageunicode-math

defaultfontfeatures Scale = MatchLowercase, Ligatures = TeX 
setmainfontSTIX Two Text[Scale = 1.0]
setmathfont[StylisticSet = 2]STIX Two Math

newcommandcsquaremathbinvysmblksquare

begindocument
( f csquare g )
enddocument

If you want to use a math font that doesn’t have this symbol, or has an ugly one, you can substitute the square from any other font of your choice with, e.g. setmathfont[range=smblksquare]Latin Modern Math.

If this is actually the cdot symbol from Lucida, you could instead define csquare by wrapping a mbox inside mathbin, or with DeclareMathSymbol.