Topology is a significant part of mathematics that focuses on spatial properties preserved under continuous deformations of objects, like stretching. (Tearing or gluing would not be allowed.) The subject was engendered from concepts in geometry and set theory, such as space, dimension, and transformation.
If you think the study of topology is far removed from the "real" world in which we live, you are mistaken. Applications of topological studies pervade all areas of our lives. For example, the surface of a golf ball has interesting topology, and manufacturers of golf balls hire mathematicians to do research on the design of golf ball surfaces that will lead to cutting edge performance through improved flight characteristics.
Topics that students in topology will study include:
MIT's Open Courseware has several entire courses in topology available to students for free, including Introduction to Topology. Many books on this subject can be found at Google Books and Amazon.com. Good tutorials on topology are available through the University of Illinois at Urbana-Champaign's Beckman Institute for Advanced Science and Technology, Topology Tutorial I. Journals that students should be following include Oxford University Press' Journal of Topology and Elsevier's Topology.
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