I think Goq’s comment answers all the different commenters here perfectly.
Be kind to everyone.
Be kind to your single neighbor, divorced or other, by extending an invitation.
Try to help all your neighbors in whatever way you can when you see a need arise.
Try to offer the help and invitation in a sincere, nonintrusive way.
Don’t be a yenta and ask too many questions.
Don’t make the other person feel like a nebach.
And to the people on the receiving end-
Don’t make assumptions about people offering help. In all likelihood, they’re extending a hand in friendship because they’d like to be your friend! Don’t decide that they’re pushy yentas who are treating you like a nebach.
Feel free to accept or decline the kind offer as you please. But don’t judge the one making the offer!
And to all of you, don’t decide that just because you like hot potato kugel, cold beer, having your seder with a lot of other people, or shoveling snow, that everyone else feels the same way.
There’s nothing abnormal about wanting to have a nice Shabbos seuda alone in your own home, and no reason to think that just because you like setting a dozen places at the table, there’s something wrong with eating alone.
Somewhere along the way we’ve become very judgmental of others and at the same time, quick to take offense at the way others approach us.
A little kindness, tolerance, open-mindedness and menchlichkeit, would go a long way towards solving a lot of our crises.
And the above can be extended (I’m sure Goq will approve) to everyone, divorcees and all our other neighbors too.