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.


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.


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.

Log in or register to write something here or to contact authors.