Abstract
In the first part we discuss metric spaces and continuous maps between them. Reformulating the notion of continuity leads to the concept of topological spaces. Some important properties of such spaces are discussed. We end with the concept of topological manifolds, as a particular class of examples of topological spaces.
The second part is a tutorial on equivalence relations and quotient sets. The main aim here is to recall a few relevant definitions in this context and more importantly make the reader comfortable with these definitions by providing a series of examples. Examples are discussed keeping in mind their significance in advanced topics of Mathematics such as topology and geometry.
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References
[1] A. Hatcher, Algebraic topology. (Cambridge University Press, Cambridge, 2002).
[2] J. R. Munkres, Topology: a first course. (Prentice-Hall, Inc., Englewood Cliffs, N.J., 1975).
[3] M. Nakahara, Geometry, topology and physics. (Taylor & Francis, Boca Raton, FL, USA, 2003).
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© 2017 Springer Nature Singapore Pte Ltd. and Hindustan Book Agency
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Basu, S., Bhattacharya, A. (2017). Set Topology. In: Bhattacharjee, S., Mj, M., Bandyopadhyay, A. (eds) Topology and Condensed Matter Physics. Texts and Readings in Physical Sciences, vol 19. Springer, Singapore. https://doi.org/10.1007/978-981-10-6841-6_2
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DOI: https://doi.org/10.1007/978-981-10-6841-6_2
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6840-9
Online ISBN: 978-981-10-6841-6
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