# Topology

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**Topology** is a particularly virulent, yet fortunately rare, strain of mathematics. Its rarity is due in large part to it residing in five dimensional space.

## Symptoms

The most common symptom of topology is confusing everyday objects with one another, such as being unable to differentiate between doughnuts and coffee cups, which obviously causes many problems for police officers. Another common symptom is being unable to differentiate between old and new jokes, which can result in repeated utterances concerning doughnuts and coffee cups. Another symptom is the loss of bladder control, necessitating the use of `rubber sheets'. Other lesser symptoms include:

- Death
- Losing one's orientation
- The ability to go through walls
- The inability to break things

In a severe case of topology one might even confuse doughnuts with abelian groups. This is called 'algebraic' topology.

## History

Topology was discovered by Leonhard Euler, the town drunkard of Königsberg, when he attempted to find his way home after a particularly long night of heavy drinking. After crossing every bridge in town exactly once, he gave up on his search and returned to the bar.

Topology itself began with the creation of imaginary particles during the season premiere of the Big bang theory. During the episode, infinitesimally small strings were created from the collision of two "branes" in eleven dimensional space which, depending on their radial frequency and axial frequency, clumped into doughnut-shaped and sphere-shaped stars. It is believed that asymmetry led to the annihilation of star torii by the much more normal stars, and thus all we see in space are spheres.

Topology is important because it showed that planets show up in surprising places. They can be incredibly small and fit in the palm of your hand. But, the most important discovery of all is this: *Sophia is an imaginary planet.* The scientific implications of this will be bountiful.

## Mathematical definition

Let an object *X* be within the known universe. Then it is either a bread roll or a doughnut.

## Algebraic topology

A branch of topology where one studies algebraic problems such as "given two cups of coffee and four doughnuts, how many coffee cups and/or doughnuts do you have?" Some claim that two coffee cups is eight. A standing conjecture suggests these operations are independent under rubber sheets, and one expects a lot of excitement to come out of this.

## Examples of topological constructs

- French fries
- De-wormholing tablets
- Centerfold
- Potatoes
- Potato chips
- Triangles
- Oscar Wilde
- Rhombicuboctahedron
- Pentagon
- Sporks

## Topology Topics

- Anything with a large number of attributes named after mathematicians is
*normal*. - Any object is homeomorphic to another object if a topoligist says so.
- A compact manifold is stored more tightly than one that is not compact
- A connected space is not unconnected
- A sphere of any size can be sliced into a finite number of pieces which come together in such a way as to form the same sphere.
- If one had a ball covered in hair and attempted to comb the hair on the ball, that person would not be
*normal*.

**Glossary of mathematical terms**