Abstract
Topology is the branch of geometry which studies the properties of figures under arbitrary continuous transformations. Just as ordinary geometry considers two figures to be the same if each can be carried into the other by a rigid motion, topology considers two figures to be the same if each can be mapped onto the other by a one-to-one continuous function. Such figures are called topologically equivalent, or homeomorphic, and the problem of deciding whether two figures are homeomorphic is called the homeomorphism problem.
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© 1993 Springer-Verlag New York Inc.
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Stillwell, J. (1993). Introduction and Foundations. In: Classical Topology and Combinatorial Group Theory. Graduate Texts in Mathematics, vol 72. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4372-4_1
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DOI: https://doi.org/10.1007/978-1-4612-4372-4_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97970-0
Online ISBN: 978-1-4612-4372-4
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