Fixed point theorems - Phd Seminar
Abstract: Here is a problem to introduce the subject. A 10 foot snake (considered one dimensional) goes to its bed, also 10 feet long (and one dimensional), so that at bedtime the snake completely fills the bed. During the night it twists and tumbles in the bed, and as a result, when it wakes up in the morning, the snake will no longer be in the same position as in the evening. It may not even completely fill the bed. The problem is to show that, nonetheless, some point of the snake will be at exactly the same location in the morning as it was at bedtime.