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A pedagogical history of compactness
Umeå University, Faculty of Science and Technology, Umeå Mathematics Education Research Centre (UMERC).
2015 (English)In: The American mathematical monthly, ISSN 0002-9890, E-ISSN 1930-0972, Vol. 122, no 7, 619-635 p.Article in journal (Refereed) Published
Abstract [en]

Compactness is a central notion in advanced mathematics, but we often teach the concept without much historical motivation.  This paper fills in many of the gaps left by the standard textbook treatment, including what motivated the definition, how did the definition evolve, and how can compactness be expressed in terms of nets and filters.

Place, publisher, year, edition, pages
2015. Vol. 122, no 7, 619-635 p.
Keyword [en]
Compact, Compactness, History of Analysis, History of Topology
National Category
Other Mathematics
Research subject
Mathematics; didactics of mathematics; History Of Sciences and Ideas
Identifiers
URN: urn:nbn:se:umu:diva-106686DOI: 10.4169/amer.math.monthly.122.7.619ISI: 000370068500001OAI: oai:DiVA.org:umu-106686DiVA: diva2:844002
Available from: 2015-08-03 Created: 2015-08-03 Last updated: 2017-12-04Bibliographically approved

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fulltext(691 kB)178 downloads
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Raman-Sundström, Manya

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf