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| rdfs:comment | - This page contains resources about Geometric Topology and Topology in general.
- A topology is the layout of a network.
- Topology is a modern branch of mathematics which formalizes the processes of stretching and deforming without tearing, as well as of cutting and pasting to construct new spaces, new geometries. It is called the treatise of position and continuous phenomena. Popularizations of topology have described it as rubber-sheet-geometry, where the concept of position is key, instead of distance. In the language of category theory, topology studies the category consisting of objects called topological spaces and the morphisms which correspond to continuous mappings and homeomorphism between the objects.
- 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:
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| abstract | - 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.
- This page contains resources about Geometric Topology and Topology in general.
- A topology is the layout of a network.
- Topology is a modern branch of mathematics which formalizes the processes of stretching and deforming without tearing, as well as of cutting and pasting to construct new spaces, new geometries. It is called the treatise of position and continuous phenomena. Popularizations of topology have described it as rubber-sheet-geometry, where the concept of position is key, instead of distance. The term topology refers also to the configuration of objects (and gives information) which helps to determine better stages for functioning. In informatics it is common to hear about the topology of a network of computers. Modern abstract work with sophisticated application to physics, are -for example- knot theory and 3-manifolds. In the language of category theory, topology studies the category consisting of objects called topological spaces and the morphisms which correspond to continuous mappings and homeomorphism between the objects. Subjects of study split topology into the non-disjoint sub-topics
* point-set topology
* algebraic topology
* differential topology
* geometrical topology
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