Concepts In Topology e-bog

Topology is a major area of mathematics concerned with properties that are preserved undercontinuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing, although the notion of stretching employed in mathematics is not quite the everyday notion: see below and the definition of homeomorphism for details of the mathematical notion. Topology emerged through the development of concepts from geometry and set theory, such as space, dimension, and transformation. Ideas that are now classified as topological were expressed as early as 1736. Toward the end of the 19th century, a distinct discipline developed, which was referred to in Latin as the geometria situs or analysis situs. This later acquired the modern name of topology. By the middle of the 20th century, topology had become an important area of study within mathematics. The word topology is used both for the mathematical discipline and for a family of sets with certain properties that are used to define a topological space, a basic object of topology. The texts are arranged in a lucid form and written in colloquial English. All the essential aspects of this subject have been included. Hopefully, the present study will prove very useful for students and teachers.