Compact

Show that if there exists a continuous function from the real line to the real line when k is a compact subset of the real line and the inverse of a function on k is not compact.

I stared at this question for nearly 30 - 40 minutes then suddenly came up for air. I went straight for a cigarette and tuned in on "VH1's Greatest 100 Songs of the 80's" ... so much more interesting than compactness of inverse functions. Salt n Pepa, Beastie Boys, Young MC, Prince, Tone Loc, Men at Work, Bruce, Bobby Brown, ... the list goes on. I began belting out songs as if I teleported to Zanmai on a Saturday night. Playing my air guitar, running around my apt, I eventually slipped, feel over and caught the edge of the table. Dizzy, strange flashbacks of my childhood came racing back ... spin the bottle, roger rabbit, running man, Cory Feldman, Corey Haim, "rad", commordore 64, McDonald's menu song, slap bracelets, parachute pants, Silver Spoons, Optimus Prime ... When I regrouped, I threw myself back onto the couch, looked down at the table ... compact sets! Where am I?

I'm not getting enough sleep. I've been drinking more and more coffee. I'm writing more and more emails at work ... which just means I'm receiving three times as many that I received the previous day. I'm missing deadlines. I'm becoming disorganized. Above all, Mike Tyson wants to fight women ... come on! Random, I know!

Two hours later, I finally wrote my proof. I read it over and over and over ... and each time I read it to myself, I felt slightly intellegent. There's a fine line between feeling smart and being smart ... I wasn't anywhere close. I only felt smart because I wrote something down and not because it's at all correct. Obviously, I should go to bed .... Happy Halloween!!