Should I text her for closure so I can finally move on?

Anonymous
I was dating this girl for just over a month and things ended kinda suddenly--she claimed it was due to the long distance (we live about 2 hours away from each other). It's been a month since she ended things and we haven't even contacted each other since.

I'm really having trouble moving on and I think it's because there was no closure and I'm holding onto possibility that she still has feelings for me but she's still scared. I truly dont think I can move on until I hear her from her that she has moved on. But I dont know how to do this without coming across as desperate--I mean anytime someone breaks things off with you your ego/confidence takes a hit so hearing this again from her might help me move on but at the same time take a toll on my already dwindling self confidence. Let it be or seek closure?
Should I text her for closure so I can finally move on?
3 Opinion