blueollie

somewhat crazy this week

I am going to have to rummage through archives for things in my personal history and talk to my bank. And I can’t forget about classes and the like.

One thing that I am thinking about: consider the two point set F = \{0, 1 \} and declare each individual point to be an “open set” (this is called the “discrete topology”. ) Pretty boring, huh?

Now consider F \times F \times F..... = \Pi^{\infty}_{i=1} F_i in the product topology. Seriously, this topological space is anything but boring, as simple as it appears to be. The elements of it are simply sequences of 0’s ans 1’s. There is more here.

These things appear all over the place in mathematics including in chaos theory.

Now to run and lift a little bit and get busy.

But yeah, these are all pictures which depict this space in one or more of its common forms:

cantor2

cantor3

cantor4

cantor5

cantor6

cantor7

cantor8

cantoreggs

cantorset

cantor9

cantor10

cantor11

April 14, 2015 - Posted by | mathematics |

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