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January 04, 2007



Done and posted on my site!


I was very afraid this week when I clicked random and you know why....

Thankfully, the cosmos did not collide like it did last week:


Connected space

Connected and disconnected subspaces of R². The space A at top is connected; the shaded space B at bottom is not.In topology and related branches of mathematics, a connected space is a topological space which cannot be represented as the disjoint union of two or more nonempty open spaces. Connectedness is one of the principal topological properties that is used to distinguish topological spaces. A stronger notion is that of a path-connected space, which is a space where any two points can be joined by a path.

It is usually easy to think about what is not connected. A simple example would be a space consisting of two rectangles, each of which is a space and not adjoined to the other. The space is not connected since two rectangles are disjoint. Another good example is a space with an annulus removed. The space is not connected since you cannot connect two points, one inside the annulus and the other outside; hence the term "connect".

I don't understand.

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