Is it permissible for me to stop praying to open the door if no one else is in the house?

If the prayer is supererogatory (nafila), there is no harm in interrupting it to find out who is knocking at the door. However, in obligatory prayer (fard), one should not hasten to interrupt it unless it is for something important that is feared to be missed. It is preferred to alert by glorifying Allah (tasbeeh) for men and clapping for women. If no one hears, then it is permissible to interrupt the prayer out of necessity, especially in supererogatory prayers. As for obligatory prayers, it is permissible to interrupt them if the knocker is for an important matter, and then the prayer should be restarted from the beginning.