IO, on this forum I believe you have 4 days in which to edit, or delete, a post that you've made. If I recall correctly, if the deleted post is the only one in the thread, the thread (and thread title) will remain visible but the body of the post will be blank. I don't believe that members have the authority to delete a thread (topic), even if their's was the only post contained in it. I've never been on a forum where a member could delete a topic that others had posted to.
In the Trading Post area, a member has authority to close a thread he has started.
I hope this information is essentially correct and is of use to you.