Access

You are not currently logged in.

Access JSTOR through your library or other institution:

login

Log in through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Journal Article

On Functions Whose Graph Is a Hamel Basis

Krzysztof Płotka
Proceedings of the American Mathematical Society
Vol. 131, No. 4 (Apr., 2003), pp. 1031-1041
Stable URL: http://www.jstor.org/stable/1194180
Page Count: 11
Were these topics helpful?
See something inaccurate? Let us know!

Select the topics that are inaccurate.

Cancel
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Add to My Lists
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On Functions Whose Graph Is a Hamel Basis
Preview not available

Abstract

We say that a function h: R→ R is a "Hamel function" (h∈ HF) if h, considered as a subset of R2, is a Hamel basis for R2. We prove that every function from R into R "can be represented as a pointwise sum of two Hamel functions". The latter is equivalent to the statement: for all f1,f2∈ R R there is a g∈ R R such that g+f1,g+f2∈ HF. We show that this fails for infinitely many functions.

Page Thumbnails

  • Thumbnail: Page 
1031
    1031
  • Thumbnail: Page 
1032
    1032
  • Thumbnail: Page 
1033
    1033
  • Thumbnail: Page 
1034
    1034
  • Thumbnail: Page 
1035
    1035
  • Thumbnail: Page 
1036
    1036
  • Thumbnail: Page 
1037
    1037
  • Thumbnail: Page 
1038
    1038
  • Thumbnail: Page 
1039
    1039
  • Thumbnail: Page 
1040
    1040
  • Thumbnail: Page 
1041
    1041