Change search
CiteExportLink to record
Permanent link

Direct link
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
From the Axiom of Choice to Tychono ’s Theorem
Örebro University, School of Science and Technology.
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

A topological space X, is shown to be compact if and only if every net in X has a cluster point. If s is a net in a product Q 2A X, where each Xis a compact topological space, then, for every subset B of A, such that the restriction of s to B has a cluster point in the partial product Q 2B X, it is found that the restriction of s to B [ fg – extending B by one element 2 A n B – has a cluster point in its respective partial product Q 2B[fg X, as well. By invoking Zorn’s lemma, the whole of s can be shown to have a cluster point. It follows that the product of any family of compact topological spaces is compact with respect to the product topology. This is Tychono’s theorem. The aim of this text is to set forth a self contained presentation of this proof. Extra attention is given to highlight the deep dependency on the axiom of choice.

Place, publisher, year, edition, pages
2015.
Keyword [en]
Urvalsaxiomet, Tychonoffs sats, Zorns lemma, topologiskt rum, kompakthet
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-44729OAI: oai:DiVA.org:oru-44729DiVA: diva2:814800
Subject / course
Mathematics
Supervisors
Examiners
Available from: 2015-06-03 Created: 2015-05-28 Last updated: 2017-10-17Bibliographically approved

Open Access in DiVA

fulltext(221 kB)151 downloads
File information
File name FULLTEXT01.pdfFile size 221 kBChecksum SHA-512
dc8065f464a00b43b5f55a1095b0eb9b50e8ac9116ed918c1e039999e3c5b02ab975ad8fa5361f33beed158338334cb9d8304c37e52a50724eb96cf3ec68e560
Type fulltextMimetype application/pdf

By organisation
School of Science and Technology
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 151 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

urn-nbn

Altmetric score

urn-nbn
Total: 143 hits
CiteExportLink to record
Permanent link

Direct link
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