The branch of mathematics concerned with the study of the properties of the geometric configurations which remain invariant under transformation by continuous mapping.
Topology studies properties like nearness (i.e. neighborhood relations), deformations through local or global expansion or contraction, equivalence of forms from a geometrical viewpoints, etc…
Basically, as stated by R. ROSEN, topology studies the notion of continuity (1979, p.179).
That which remains invariant in such cases is the proximity relation between points, in such a way that there are neither ruptures or fusions as a result of the transformations. Thus distortions like pulling, bending, stretching (but not tearing) do not affect the topological properties of figures.
This type of transformations is called homeomorphisms.
Topology studies qualitative properties related to the relative positions of geometric species, independently of their form or dimensions.
Topology was originally called by H. POINCARÉ "Analysis Situs", or situational geometry and developed by him.
In Bertalanffy's words it is a study of relational mathematics including nonmetrical fields such as networks and graphs theory.
Topology is useful for constructing general models of structures and their continuous transformations.
It is suggestive that some biologists, around 1928-1935, as WOODGER, NEEDHAM and WADDINGTON, sensed the possibility and the need (in BERTALANFFY's words) of a non-quantitative mathematics, or "configuration mathematics" which would give priority to concepts of form and order.
It can be used to study basic nonnumerical relations between the elements of organized systems and the relative stability or unstability of their structures.
Topology concerns itself with concepts like: attractors, basin, enveloppe, partition, trajectory, vicinity, etc… (C. BRUTER, 1974).
Catastrophes, fractals, graphs, and groups, are related mathematical concepts.
- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
- 4) Human sciences
- 5) Discipline oriented
To cite this page, please use the following information:
Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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