Abstract
This chapter is probably the most important of the course. Although the definition of compact spaces (§1) suggests no intuitive image, it is a very fruitful definition (see the properties of compact spaces in §§2 and 3, and the applications in nearly all the rest of the course). In §4, we adjoin to the real line R a point + ∞ and a point − ∞ so as to obtain a compact space, the ‘extended real line’ ̅R; the student has made use of this for a long time, even though the terminology may appear to be new.
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© 1984 Springer Science+Business Media New York
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Dixmier, J. (1984). Compact Spaces. In: General Topology. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4032-5_4
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DOI: https://doi.org/10.1007/978-1-4757-4032-5_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2823-8
Online ISBN: 978-1-4757-4032-5
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