Topology

Topology aware or informed of the vacuum or place a Greek word (from topos means place and logos meaning study) means changing study groups that do not change the nature of theContents. Prompting some mathematicians and engineering to call engineering rubber.

Topology cares to study the spatial characteristics of spatial properties according to continue bilateral abnormalities (without ripping tensile), these properties are usually defined Non-inequalities topological, founded this branch of mathematics in the early twentieth century, taking in its evolution from 1925 to 1975 where he witnessed the maturity and posed KachtsasIntegrated.

Mobius strip

We can say that if we want this simplistic science cares sporting characteristics that are not affected when the transition from athlete to another space.

We can also say that the topology is a scienceWho is interested in studying topological characteristics transmitted to the vacuum of space by another Alchakl. To understand the meaning of the word Alchakl we say about the function of what it constitutes isomorphismIf the function is continuous and the inverse image also has an ongoing, comprehensive and differentiated.

Ataiwbolgaa theories (formulations) in modern mathematics, which originated in the nineteenth century and crystallized in the twentieth century.

Although its roots in engineering the mathematical analysis of its growth, but he rode with them and has now become a tool for all of mathematics.

Topology has grown from an engineering aspects, as in the topology synthesis (harmonic) combinatorial by Euler and August Ferdinand Mobius and Felix Klein the Riemann and crystallized by Henri Poincare. Grew from mathematical analysis and as an extension of the theory of groups as in the analytical Topology (year), and then follow the growth of the two lines, one Areas to be considered to topological spaces as generalized geometric configurations and be focused on the installation of the blanks themselves, and these areas Introduced (algebraic topology) at the hands of Ailanberg and Stanrod (1930), and at the hands of Alhomuljia Oalnberg (1945), and studies Folding raised by the work of Henry Poincare (1900), and dimensional theory raised by the work of Riemann (1850-1870).

The second line in mathematical analysis where it is seen to space Khamlh of Douala, where the continuous functions occupies the continuing importance. It is this Fields theory Banach, and Hilbert spaces, and Ghebreat Banach, and the modern theory of integration (integration of Obeg), and the theory of measurement, harmonic analysis and modern functional analysis.

Ohz topology shows that became the basis for most contemporary mathematics. In general, the theoretical premise for all types of topology is the installation of the vacuum topological and Topology Analytical (year).

The Cantor of Alawil inventors of analytical topology, introduced the study of partial classes of topological vacuum and gave them the basic concepts of topology such categories Sealed and open categories and narrow-mindedness, and the end point and the inside and outside ... especially on the number line.

As defined by the vacuum topological groups and so-called open topology categories open point set topologe feet simply Kazimierz Kuratovski (1922), and byNeighboring feet simply Felix Hausdorff (1914). Preceded by The hypothesis (1906) and Rest (1907-1908) in the definition of topological vacuum through the convergence of sequences butTheir definitions were not satisfactory, and gave Andrei Kolmogorov (1935) and Rest (1907), and Hawsdrof (1914), and Chinov (1930) types of topological spaces on the basis ofAxioms of separation.

Simply species (branches or core areas of topology):

Analytical topology (topology classes blobs),

Geometric Topology (synthesis).

Topology forced.

Date topology

The beginnings of the topology in the search for answers to questions of engineering in the mid-eighth century. The question raised by the world's major sports Leonhard Euler in1736 entitled Konigsberg bridges seven first academic paper in the topology.

The seven bridges of Konigsberg issue very famous was solved by Leonhard Euler It was the use of the word topology for the first time in Germany in 1847 by the German mathematician Johann Benedict listings The English word has emerged first Once in 1833 in the journal Nature (patrol) British. During the period between the late nineteenth century and the mid-twentieth century has been the development of several books Established the topology to be mathematically independent note. The topology is based largely on the modern theory of groups. Among the most famous scientists in the early century topology Twenty great scientist Felix Hausdorff who introduced in 1914 the concept of topology spaces and will know later as the space Hausdorff.