Abstract
After reviewing in §1 certain concepts already known concerning metric spaces, we introduce topological spaces in §2, then the simplest concepts associated with them. For example, one has an intuitive notion of what is a boundary point of a set E (a point that is ‘at the edge’ of E), a point adherent to E (a point that belongs either to E or to its edge), and an interior point of E (a point that belongs to E but is not on the edge). The precise definitions and the corresponding theorems occupy §§4 and 5. Separated topological spaces are introduced in §6; on first reading, the student can suppose in what follows that all of the spaces considered are separated.
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© 1984 Springer Science+Business Media New York
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Dixmier, J. (1984). Topological Spaces. In: General Topology. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4032-5_1
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DOI: https://doi.org/10.1007/978-1-4757-4032-5_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2823-8
Online ISBN: 978-1-4757-4032-5
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