Topology is the branch of mathematics that analyzes notions such as continuity, convergence and connectivity.
The term topology is used to identify an area of mathematics that studies continuity and other concepts originated from it. It is a specialization linked to the properties and characteristics that geometric bodies possess and that remain unchanged thanks to continuous changes , regardless of their size or appearance.
It should be noted that the continuous functions of mathematics are those that, at nearby points in the domain, experience small variations in values . At a graphic level, these functions are usually able to be drawn without having to lift the pencil from the paper.
Another central concept of topology is topological space , a mathematical structure that allows continuity, connectivity and convergence, among other concepts, to be formally defined.
What is topology
Topology, therefore, is the specialization that focuses on the study of continuous functions and topological spaces. This discipline works with objects in different ways, as long as the aforementioned continuity is not interrupted. In everyday language, it could be said that topology is allowed to bend, stretch, twist or shrink elements, but without breaking them or segmenting what is joined or gluing what is separated.
At a topological level, a triangle is the same as a circle: one can be transformed into the other continuously, without the need to cut or paste. On the other hand, a circle can never be transformed into a segment from a topological point of view, since such a transformation would require breaking the continuity of the figure .
Among the branches of topology, it is possible to distinguish general (also called conjunctive ), differential and algebraic .
In computing, topology is linked to the structure that a network adopts.
The concept and communication networks
In the field of computing, network topology represents a set of computers communicating with each other for the exchange of information, where each one is called a node. Two possible "figures" that adopt this type of systems are defined below:
* star : each node is connected to a central one, reducing the risk of errors in the network. In this way, for the surrounding nodes to communicate with each other, they depend on sending the data to the one who connects them; This is responsible for transmitting them to the rest. In case of emergent behavior on the part of the system that sends the information, only that packet is lost, without affecting the other processes .
If, however, the failure occurred in the central node, the problem would be general and this shows the high level of vulnerability that this type of design presents. On the other hand, the central node must carry out a large volume of work, which grows proportionally to the number of nodes that connect to it, so this topology is not appropriate in the case of very extensive networks.
* tree : Building on the previous concept, this topology presents a design that connects a series of star networks and arranges them hierarchically. In this way, there are various central nodes, which distribute the functions. If there is a problem with one of the "sheets", it is isolated; If the failure is in a complete section, then it becomes inoperative, but it does not affect the rest of the tree, unlike what was previously explained.
Thanks to more advanced indexing and node identification techniques than those used in a star network, as well as being able to avoid system collapse by adding more central nodes, this topology offers more efficiency and is potentially impossible to saturate. In any case, the tree is not justified in the case of small structures, since it requires very expensive maintenance.