Check out these photos, obtained by TMZ, which we're told were shot Friday at a multi-purpose gym facility near Thousand Oaks, CA ... where their eldest daughter, North, was playing in a league basketball game for kids around 7 PM.

There's mom and dad in the stands ... looking on as North does her thing with her team. They weren't even that far apart -- just a row back from one another, in very close proximity.

Eyewitnesses tell us they did speak from time to time throughout the evening, and appeared to be cordial. Neither parent made a big scene by cheering or much of anything else ... we're told they looked like they were just trying to lay low and just watch North together.

This is definitely a good sign of successful co-parenting, which Kim and Kanye had already shown they can do without issue. Remember, they did this exact sort of thing back in March when they hit up Saint's soccer game in the same crew. There, too, they looked OK.

That was during a time when Kanye was raging online as Pete and Kim's relationship was getting more serious ... but since then, he's calmed down a lot and been mostly silent.

Of course, much has changed in the months that have followed ... including the undeniable fact that PD has not only met Kim and Kanye's kids, but has gotten pretty close with them as well -- evidenced in a recent one-on-one outing he had with their son at The Grove.