What are a few examples of mathematical objects which have the word "pseudo" used in the definition?

Question

As motivation for this question, I wanted to create a short slide-show presentation for students on how mathematicians use the word pseudo.

Wherever we see the word pseudo, two different definitions are presented.

Number	General	Specific Example
1	a definition for a small set of mathematical objects	a definition of what a desk is
2	a definition for a broader larger set of mathematical objects	a definition of what a pseudo desk is, including dining tables and other furniture items with a flat surface on the top.

That is not a mathematical definition.

My question is, what is an example of a definition published in a real book or real research paper which used the word "pseudo"?

I have seen such things, but I have forgotten most of the details.

---

Answer 1

Actually this is not how the word "pseudo" gets used. Typically a pseudo-X refers to something that is like an X but not actually an X, and such that Xes are not pseudo-Xes. So it is not (usually?) a generalization of X. For example:

• a pseudovector is like a vector, but vectors are not pseudovectors. Similarly a pseudoscalar is like a scalar, but scalars are not pseudoscalars.
• a pseudonatural transformation is like a natural transformation. I suppose in this case it does give natural transformations as a special case.
• a pseudogroup is like a group, but groups are not pseudogroups (actually it is a kind of groupoid).

There are also a few other similar prefixes, such as "quasi-" (although this does sometimes refer to a generalization), "pre-" (also a generalization), or, more rarely, "fake" (explicitly not a generalization).

Answer 2

There's also pseudoprimes, which are natural numbers that share some particular property with primes (typically one that is used in primality tests) but are not primes. For example, Fermat pseudoprimes to base $b$ are composite numbers $x$ that divide $b^{x-1} - 1$.