Topology definition - What it is, Meaning and Concept

The term topology is used to identify a area of ​​mathematics that studies continuity and other concepts originated from it.It is a specialization linked to the properties and characteristics that the geometric bodies possess and that remain unchanged thanks to continuous changes , regardless of their size or appearance.

It fits Note that the continuous functions of mathematics are those that, in the near points of the domain, experience small variations in the values.On a graphic level, these functions are usually in a position to be drawn without the need to lift the paper pencil.

Another central concept of the topology is the topological space , a mathematical structure that allows for a formal definition of continuity, connectivity and convergence, among other concepts.

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 the words of everyday language, it could be said that the topology is allowed to bend, stretch, twist or shrink the elements, but without breaking them or segmenting what is attached or pasting what is separated.

At the 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; instead, a circle can never be transformed into a segment from a topological point of view, since such transformation would require breaking the continuity of the figure.

Among the branches of the topology, it is possible to distinguish general (also called conjunctist ), the differential and the algebraic .

Topology and communication networks

In the field of informatics, the network topology represents a set of computers communicated with each other for the exchange of information, where each one is called a node.Next, two possible “figures” are defined that adopt this type of systems:

* star: each node is connected to a central one, reducing the risks of errors in the network.Thus, so that the surrounding nodes communicate with each other, they depend on sending the data to which it connects them; This is responsible for transmitting them to the rest.In case of emergent behavior by the system that sends the information, only that package is lost, without this affecting the other processes.

If instead the failure if the central node occurs, the problem would be general and this demonstrates the high level of vulnerability that this type of design presents.On the other hand, the central node must perform a large volume of work, which grows proportionally to the amount of nodes that connect to it, so this topology is not suitable in the case of very large networks.

* tree: starting from the previous concept, this topology presents a design that connects a series of star networks and arranges them hierarchically.In this way, there are several central nodes, which distribute the functions.If there is a problem with a from the "leaves", it is isolated; if the fault has a complete section, then it becomes inoperative, but does not affect the rest of the tree, unlike the above.

Thanks to indexing techniques and identification of nodes more advanced than those used in a star network, as well as being able to avoid the collapse of the system 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.