Drop his mother a quick note or email after the split: Tell her you're sorry about what happened partly because you like her so much and are hoping this doesn't mean your friendship has to end. Then back off and wait for her to reply. If she doesn't, take the hint. If she does, but doesn't suggest getting together, take the hint. If she invites you to grab a latte, feel free, but realize that things could be awkward since at least some of what you had in
common before was her son, about whom anything but casual conversation should probably now be limited. If you still have things to talk about (you both love dogs and can yak for an hour about dalmatians, for instance) there's hope that the friendship can actually rise above all that's working against it. But, alas, that would be a rarity. In any event, make sure the pursuit is mutual—a fine rule of thumb in every relationship.
His take: As a formerly jilted boyfriend, I feel compelled to speak up for the missing person amid your series of concerns: your ex-boyfriend. He's the one being rejected here, so when it comes to wondering about any subsequent relationship with his mother, I suggest you start your investigation with him. If he says, "Well, gee, it wouldmake me kind of uncomfortable if you were to keep meeting my mom for lunch on Tuesdays at the Olive Garden," then you have your answer. You have no obligation to his mother and should expect nothing from her going forward. To do so would make your ex feel even worse than I assume he already does. Most people need a clean break in a breakup, and any continuing relationship you have with his mother could end up dangling your existence in front of him just when he'd like to forget you. His mother must know this, too. So the two of you ought to acknowledge that fact, hug each other goodbye, and let the friendship go. If, however, your ex says it doesn't bother him if you and his mother want to remain in each other's lives, or if he even encourages it, your next move should be to approach the mother about it. (As a direct relative of the dumpee, her feelings come next in the pecking order. As the dumper, your feelings come last.) You should be prepared for the possibility that she could be feeling hurt—not to mention protective of her son—and you may find that she's not so "extremely close" to you after all. (It might also be wise to suspect your ex of trying to maintain a connection to you through his mother.)
But let's say she's on board for keeping things going, and you don't doubt your ex's motives. Then you may want to take a serious look at your own feelings. As in, "Do I really want this woman telling me, six months from now—over pasta and salad—that her son is still in love with me, that we were really great together, and why not give it another shot?" You know how it's better to rip a Band-Aid off than to remove it slowly? Well, sometimes you have to rip off two of them.