Is there a convention which rules that in mathematics an object with some properties should be referred to as a

"property 1 property 2 property 3 ...object"

rather than a

"property 1, property 2, property 3, ...object"?

Specific example is an "oriented compact smooth manifold". By googling this question I found that it would appear the convention is without commas, but I could not find a source confirming that it actually was.

Can someone confirm this is the correct convention, and perhaps from which organization the convention comes from?

I hope this falls within the bounds of MathStack; although it is obviously not about mathematics per se, I'm guessing nearly everyone on this site has written something like what I'm asking about!

  • $\begingroup$ It's preference, really. $\endgroup$ – Alex Provost Jul 10 '13 at 18:17
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    $\begingroup$ Well I would have said the same thing before I googled it. If you click the link, you will see 9 hits with no commas, 0 with commas. $\endgroup$ – levitopher Jul 10 '13 at 18:25
  • $\begingroup$ "no commas" suggests that the reader can readily make sense of the entirety as one object. "commas" suggests that the reader see this object as a special case of a special case of objects. The former is more likely to be used in more mature fields where it has been used a long time. $\endgroup$ – vadim123 Jul 10 '13 at 18:29

This has nothing to do with mathematics or the mathematical objects in question.

Note that in this case compact, smooth and even oriented are all adjectives.

I forward you to the concepts cumulative adjective and coordinate adjective.

What's below was copied from this link.

This link from English SE should also be useful.

Coordinate Adjectives

These are adjectives that separately modify a noun. Their order can be scrambled and they can be joined by and. A comma is needed to separate each coordinate adjective. But if there is a the word and no comma is needed.

Example: While strolling in the woods, they found a strange, mysterious and frightened child.

Cumulative Adjectives

When adjectives pile up to jointly describe the noun and need to be arranged in a specific order, they are called cumulative adjectives. No commas are needed to separate the adjectives.

Example: He bought a wonderful old French car.

Cumulative adjectives generally follow a certain order of arrangement. $$ \begin{array}{c|c|c|c} 1. & \text{Opinion} & \text{good, attractive, beautiful, delicious, }\ldots \\ \hline 2. &\text{Size} & \text{large, small, enormous, }\ldots \\ 3. & \hline \text{Age} & \text{old, new, modern, young, }\ldots \\ \hline 4. & \text{Length or shape} & \text{long, short, square, round, }\ldots\\ \hline 5. & \text{Color} & \text{red, blue, green, }\ldots\\ \hline 6. & \text{Origin (nationality, religion)} & \text{American, French, Muslim, Christian, }\ldots \\ \hline 7. &\text{Material} & \text{plastic, woolen, wooden, cotton, }\ldots \\ \hline 8. & \text{Purpose} & \text{electric (wire) , tennis (shirt), }\ldots \end{array}$$

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    $\begingroup$ very interesting, and probably what I'm looking for. So the rule would be more general to more specific if the order mattered, but the order does not frequently matter (as in the case of "oriented compact smooth manifolds") so either one is appropriate. $\endgroup$ – levitopher Jul 11 '13 at 15:25
  • $\begingroup$ I had a similar question and found this informative, however I think the conventions are a little different for mathematical writing than they are for general English. For instance, both "finite-volume compact orientable manifold" and "orientable finite-volume compact manifold" are just fine, but one would not typically see "finite-volume, compact, orientable manifold," or the like. $\endgroup$ – j0equ1nn Nov 18 '16 at 3:23

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