Strict inequality in the box-counting dimension product formulas

Article

Robinson, J. and Sharples, N. 2012. Strict inequality in the box-counting dimension product formulas. Real Analysis Exchange. 38 (1), pp. 95-120.
TypeArticle
TitleStrict inequality in the box-counting dimension product formulas
AuthorsRobinson, J. and Sharples, N.
Abstract

We supplement the well known upper and lower box-counting product inequalities to give a new product formula for subsets of metric spaces. We develop a procedure for constructing sets so that the upper and lower box-counting dimensions of these sets and their product can take arbitrary values satisfying the above product formula. In particular we illustrate how badly behaved both the lower and upper box-counting dimensions can be on taking products.

PublisherMichigan State University Press
JournalReal Analysis Exchange
ISSN0147-1937
Electronic1930-1219
Publication dates
Print2012
Publication process dates
Deposited15 Oct 2015
Accepted22 Mar 2012
Submitted22 Sep 2011
Output statusPublished
Accepted author manuscript
Additional information

Vol.38 • No. 1 • 2012/2013

Web address (URL)https://projecteuclid.org/euclid.rae/1367265642
LanguageEnglish
Permalink -

https://repository.mdx.ac.uk/item/85zq3

Log in to edit

Download files

Accepted author manuscript
RobinsonSharples12.pdf

  • 142
    total views
  • 130
    total downloads
  • 3
    views this month
  • 6
    downloads this month

Export as

Related outputs

Public engagement for student empowerment
Jones, M., Kazim Ali, Z., Lawrence, S., Masterson, B., Megeney, A. and Sharples, N. 2025. Public engagement for student empowerment. MSOR Connections. 23 (3), pp. 83-91. https://doi.org/10.21100/msor.v23i3.1567
Making mathematicians: developing expert attitudes with authentic maths activities
Jones, M., Kazim Ali, Z., Lawrence, S., Masterson, B., Megeney, A. and Sharples, N. 2025. Making mathematicians: developing expert attitudes with authentic maths activities. MSOR Connections. 23 (3), pp. 100-113. https://doi.org/10.21100/msor.v23i3.1579
Authentic activities for making mathematicians
Masterson, B., Megeney, A. and Sharples, N. 2024. Authentic activities for making mathematicians. CETL-MSOR Conference 2024. University of Limerick, Ireland 29 - 30 Aug 2024
Public engagement for student empowerment
Masterson, B., Megeney, A. and Sharples, N. 2024. Public engagement for student empowerment. CETL-MSOR Conference 2024. University of Limerick, Ireland 29 - 30 Aug 2024
Authentic no-exam assessment for student wellbeing
Masterson, B., Sharples, N. and Megeney, A. 2024. Authentic no-exam assessment for student wellbeing. Designing Assessment to Promote Students’ Wellbeing. University of Greenwich, London, UK 10 - 10 Jul 2024
Authenticity in learning, teaching and assessment
Masterson, B., Sharples, N., Jones, M., Megeney, A. and Lawrence, S. 2024. Authenticity in learning, teaching and assessment. MSOR Connections. 22 (2), pp. 29-36. https://doi.org/10.21100/msor.v22i2.1488
Student video curation
Jones, M., Lawrence, S., Masterson, B., Megeney, A. and Sharples, N. 2023. Student video curation. MSOR Connections. 21 (2), pp. 15-24. https://doi.org/10.21100/msor.v21i2.1403
Authentic by design: developing mathematicians for the talent economy
Masterson, B., Jones, M., Lawrence, S., Megeney, A. and Sharples, N. 2023. Authentic by design: developing mathematicians for the talent economy. MSOR Connections. 21 (2), pp. 44-51. https://doi.org/10.21100/msor.v21i2.1400
Revising the role of the history of mathematics in post-pandemic world
Lawrence, S., Megeney, A., Sharples, N., Masterson, B. and Jones, M. 2022. Revising the role of the history of mathematics in post-pandemic world. Uzdanica. XIX, pp. 17-28. https://doi.org/10.46793/Uzdanica19.S.017L
Student video curation [Conference item]
Jones, M., Lawrence, S., Masterson, B., Megeney, A. and Sharples, N. 2022. Student video curation [Conference item]. CETL-MSOR Conference 2022. Abertay University, Dundee, UK 01 - 02 Sep 2022
Authentic by design: developing mathematicians for the talent economy
Masterson, B., Megeney, A., Sharples, N., Lawrence, S. and Jones, M. 2022. Authentic by design: developing mathematicians for the talent economy. CETL-MSOR Conference 2022. Abertay University, Dundee, UK 01 - 02 Sep 2022
Engaging with maths online - teaching mathematics collaboratively and inclusively through a pandemic and beyond
Jones, M., Megeney, A. and Sharples, N. 2022. Engaging with maths online - teaching mathematics collaboratively and inclusively through a pandemic and beyond. MSOR Connections. 20 (1), pp. 74-83. https://doi.org/10.21100/msor.v20i1.1322
On solutions of the transport equation in the presence of singularities
Miot, E. and Sharples, N. 2022. On solutions of the transport equation in the presence of singularities. Transactions of the American Mathematics Society. 375 (10), pp. 7187-7207. https://doi.org/10.1090/tran/8701
Digital pedagogy in a world of digital poverty: the Middlesex iPad project
Jones, M., Megeney, A. and Sharples, N. 2021. Digital pedagogy in a world of digital poverty: the Middlesex iPad project. AdvanceHE Curriculum Symposium 2021. Online 08 Jun 2021
iPads for teaching and learning mathematics: collaborative group-work in an engineering-appropriate setting.
Jones, M., Megeney, A. and Sharples, N. 2021. iPads for teaching and learning mathematics: collaborative group-work in an engineering-appropriate setting. UCLan Conference: "Supporting Engineering Students with Weak Maths Skills and Widening Participation". Online 25 Mar 2021
Collaboration and co-creation at a distance: using technology to enhance student engagement online
Jones, M., Megeney, A. and Sharples, N. 2021. Collaboration and co-creation at a distance: using technology to enhance student engagement online. AdvanceHE Student Engagement Conference 2021. Online 26 May 2021
Using technology to engage Generation Z Mathematics students
Jones, M. and Sharples, N. 2020. Using technology to engage Generation Z Mathematics students. University of South Wales: Teaching Excellence Seminars. Online 09 Nov 2020
Video recording lectures: blending the quarantini
Jones, M. and Sharples, N. 2020. Video recording lectures: blending the quarantini. TALMO Workshop: Student Engagement and Interaction. Online 03 Sep 2020
Generalised Cantor sets and the dimension of products
Olson, E., Robinson, J. and Sharples, N. 2016. Generalised Cantor sets and the dimension of products. Mathematical Proceedings of the Cambridge Philosophical Society. 160 (1), pp. 51-75. https://doi.org/10.1017/S0305004115000584
On the regularity of Lagrangian trajectories corresponding to suitable weak solutions of the Navier-Stokes equations
Robinson, J., Sadowski, W. and Sharples, N. 2013. On the regularity of Lagrangian trajectories corresponding to suitable weak solutions of the Navier-Stokes equations. Procedia IUTAM. 7, pp. 161-166. https://doi.org/10.1016/j.piutam.2013.03.019
Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations
Robinson, J. and Sharples, N. 2013. Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations. Journal of Differential Equations. 254, pp. 4144-4167. https://doi.org/10.1016/j.jde.2013.02.012