Is there a convention that forbids paragraph break immediately after a displayed math formula?

Question

Is there any typographical rule or convention that forbids paragraph break right after a displayed math formula?
For example see this code where the first displayed math formula does not have any paragraph after it and the second displayed math formula has a paragraph break right after it:
documentclass{article}
begin{document}
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec lectus
velit, dapibus ut eleifend quis, condimentum eu elit. Curabitur
scelerisque orci at lectus aliquet mattis ut ultrices massa.
$$
1 + 1 = 2
$$
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec lectus
velit, dapibus ut eleifend quis, condimentum eu elit. Curabitur
scelerisque orci at lectus aliquet mattis ut ultrices massa.

$$
1 + 1 = 2
$$

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec lectus
velit, dapibus ut eleifend quis, condimentum eu elit. Curabitur
scelerisque orci at lectus aliquet mattis ut ultrices massa.

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Donec lectus
velit, dapibus ut eleifend quis, condimentum eu elit. Curabitur
scelerisque orci at lectus aliquet mattis ut ultrices massa.
end{document}

Here is the output:

Is there any rule or convention that forbids the second displayed math formula that is followed immediately by a paragraph break.
I tried searching through a couple of popular math books published by Springer I have but I could not find a single instance of a displayed math formula immediately followed by a paragraph break and that is what made me wonder if such a style is forbidden.

David Carlisle · Answer

You should not use $$ in LaTeX, also you should not have a blank line before the display, having a paragraph break after the display is fine if the following text starts a new paragraph, although not ending a sentence with a displayed equation ovoids the old issue of how best to place the end of sentence punctuation.
If you have a blank line before the display Tex inserts a spurious one line empty paragraph before it, so it has the appearance of vertical space but is not dropped at a page break.

Is there a convention that forbids paragraph break immediately after a displayed math formula?

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