The Ghost That Woke Me Up

I used to live in a one bedroom apartment in a building probably built no early than the 1950's. I lived on the third (top) floor in a middle apartment. I noticed that there was always a cold spot on the carpet in my apartment a little ways from the door. There was not one plausible explanation as to why this spot was always cold. There was no air duct above or beneath - in fact, the building had radiator heat. And if you were alone in the apartment, you always saw something move at the edge of your vision.

One night, while I was in bed sleeping, I suddenly awoke - and for no apparent reason - no sound, no change in light had occurred (I usually kept the hall light on, and it was, as usual, still on.) The door to the bedroom was opposite the foot of my bed, and upon awakening, I saw the lower half of a person hovering - as if hanging in the air - just beyond the bedroom door frame - with the upper part of the body shielded from my view by the portion of wall above the bedroom door. I took note "How odd.." and fell back asleep. And then woke suddenly again - now the body, although still hovering, was closer to my bed and closer to the floor. This continued to happen about four times in total, until the apparition was standing next to me on the right hand side of my bed.
It was a plump old woman, wearing thick glasses, a button style hat with a face net and a woolen skirt suit, she looked dressed as if to go to church. I couldn't see her eyes through her glasses, just a little reflective glint on the lenses and behind that was gray and blank. I lay there, propped up on one elbow and we looked at each other. Then I lay down and went back to sleep.
What I had already suspected by the cold spot and the movements I saw out of the corner of my eye was confirmed, there was a ghost in my apartment. I never saw her again, but the cold spot remained and the things darting in my peripheral vision continued.