Abstract
Abstract topology studies the the notions of nearness and proximity of points by axiomatising the concept of an open neighbourhood of a point. Intuitively, an open set is one with the property that if it contains a point x, then it contains all points near x. In the hyperreal context we can make this idea quite explicit by taking “near” to mean “infinitely close”. As we shall see, this leads to a very natural formulation and treatment of many topological ideas.
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© 1998 Springer-Verlag Berlin Heidelberg
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Goldblatt, R. (1998). Topology of the Reals. In: Lectures on the Hyperreals. Graduate Texts in Mathematics, vol 188. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0615-6_10
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DOI: https://doi.org/10.1007/978-1-4612-0615-6_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6841-3
Online ISBN: 978-1-4612-0615-6
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