Topology is more general than geometry, being simply the study of CONNECTIONS (while geometry is the study of CONNECTED systems with specific SHAPE and SIZE).

We grapple with topology from the very beginning of our lives! But parents and family members and neighbors and teachers don't know enough to tell us about this. The French dramatist, Moliere, has a character in one of his plays who discovers that he's been talking "prose" all his life and didn't know it, since no one taught him the word and its meaning. Similarly, each of us has been solving topological problems every day of our lives, but may not know it because no one taught us the word and its meaning.

Edward Kasner, American mathematician and grandfather of the five-year-old boy who named "The Googol", once said that he found it easier to teach topology to tots than to grownups, because they "haven't been brain-washed by geometry"!

Here are some topological experiences of tots:

Challenge: Keep a TOPOLOGY-DIARY, listing each experience every day in coping with THE CONNECTIONS OF TOPOLOGY.

Original web page by Jon Hays.  Jon's other topological pages: