### (Topology)

A set X is called totally disconnected if each of its members is its own connected component.

The most famous example of a totally disconnected set is the Cantor set. Note that it has the cardinality of the continuum ℵ=20. Totally disconnected sets can be big, even in R! This set is homeomorphic to the topological space {0,1}N; in fact, every set FN with F finite is totally disconnected when equipped with the product topology.

Once again the opportunity has arisen to explain in simple language what's going on hereinabove.

### This is topology for the common man.

GLOSSARY:

Topology: the study of bottle caps, screw-on jar lids, catsup bottle lids, and toupees. (You see, all part of the set X="tops").

Totally disconnected: the state of being out of touch with reality. Aunt Minerva's been in and out of psychiatric hospitals for years, and she's heavily medicated. She's a delightful old dear, but is indeed totally disconnected.

Cantor set: when the singing rabbi does a few numbers, then sits down and takes a break. The typical Cantor does two sets, one at the beginning of the service, and one at the end.

Cardinality: anything to do with a certain species of bird, the male of which displays fiery red-colored plumage.

Continuum: When one cleans with a vacuum cleaner, the act is referred to as "vacuuming." I will vacuum, she vacuums, I am vacuuming, we have vacuumed. However, if one stops this act and then resumes it, one may say "I will continuum."

R!: C'mon, silly, the middle initial of "Toys Я Us," with exclamation added.

Homeomorphic: I don't know what this is, but I'm pretty sure it has to do with that Brokeback Mountain stuff.

"Equipped with the product topology:" a line used by computer salesmen to get you to buy the top-of-the-line machine that's loaded with features.

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The definition is sublime. It makes so much sense. The phrase "each of its members is its own connected component" has to do with a gentleman's, ahem, member. Any man worth his salt should be pretty damn sure that his member is a connected component. Hey, remember the gal who cut her boyfriend's member off? His member wasn't connected anymore.

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