When a breakup occurs, the two people involved go through a period of the unknown: Will we speak again? Will we see each other again? Will we come back from this? Is this final, permanent, forever? Is there any hope for us in the future? These questions are logical, sometimes unrealistic though. A typical breakup consists of two individuals parting ways, and cutting each other off, yet a lot of couples have tended to stay connected and intertwined in each other's lives, sometimes staying best friends, or friends for years.
Some are able to take some time to themselves and actually rebuild a friendship with their ex, while others find it impossible. Sometimes there is a grey area both need to move past and get over, but sometimes, rebuilding a friendship can lead to reconnecting and reigniting whatever connection/chemistry/intimacy there was once there before. It's been known to happen.
The best thing to do is to not rush into being friends right after the breakup. Each of you has to grieve and work through your own issues individually, independently. Being in a relationship is a huge commitment and once that is broken, rebuilding is needed, especially if the relationship was very serious. Start small. Baby steps. This time is critical for you and your ex because if the wrong moves are made, no kind of relationship may be able to survive between you two.
Habits die hard. When you are with someone for a long time, you build a foundation with that person. You are one way with that person, always. It is hard to cut those habits and familiarization with one another, but it is needed in order to move on the right ways. Sometimes, if you both remain single, it is easy to get caught up in the moments, and get comfortable with how you used to be, but in the end, it is not the healthiest to do because it sends mixed signals everywhere.
When you date someone, you have a type of friendship that has built into a romantic adventure. Many say if you can't be friends with someone you previously dated, there probably never was a real friendship to begin with. Not always true, but it is just how you communicate and deal with the situation. Friendship is possible after a breakup. But not for everyone. Take your time and be strong, and you'll get what you want in the end.