Gromov - Hausdorff Dimension and Measure of Separable Metric Spaces

Crossmark

Main Article Content


Abstract

In this paper, we proved that dimension of Gromov – Hausdorff hyperspace of Riemannian manifold depends on the cardinality of measurable Riemannian manifold.

Downloads

Download data is not yet available.

Citation Metrics & Similar Scopus Articles

Data source Crossref
0
citations
Citation counts are source-specific and may differ because database coverage, reference matching, and update schedules are different. Counts are not added together. Crossref values represent citation links registered and matched by Crossref.
Check Secondary Documents in Scopus
Open this article in Scopus, then check the Secondary documents tab. Use Manual Citation Fallback only for counts you have verified manually.
Open in Scopus
Similar Scopus Articles
Scopus
  1. Tsafack A.D. (2027)
    CURVE RECONSTRUCTION IN INVERSE PROBLEMS: FROM DIVERGENCE-MEASURE VECTOR FIELDS TO DENSITY LEBESGUE MEASURES
    Inverse Problems and Imaging, 26, 172-188
  2. Vural G. (2027)
    Determining the robust drivers of CO2 emissions in Africa: Machine learning and panel econometric evidence on the Environmental Kuznets Curve hypothesis
    Unconventional Resources, 17
  3. Li C. (2027)
    Topology-driven explicit–implicit EMT method with automatic dimension reduction for LCC–HVDC across physically reachable topologies
    Electric Power Systems Research, 264

Article Details

How to Cite
Morawo, M. A., D., H. A., & Y., A. K. (2025). Gromov - Hausdorff Dimension and Measure of Separable Metric Spaces. Asian Journal of Science, Technology, Engineering, and Art, 3(2), 488-496. https://doi.org/10.58578/ajstea.v3i2.5206

References

Dong, C., and Gabjin, Y. (2000). “Gromov – Hausdorff Topology and its application to Riemannia Manifold.

Fremlin, D.H. (2019). Measure theory. Volume 5. University of Essex.

Facundo, M and Zhengchao (2021). Charaterization of Gromov – type geodesics. Department of Mathematics and Computer Science and Engineering, The Ohio State University.

Facundo, M. (2012). Some properties of Gromov – Hausdorff distance. Discrete compute Geom. 48. 416 – 440.

Fell, J. (1962). A Hausdorff topology for the closed subset of a locally compact and non – Hausdorff spaces. Proc. Amer.Math.Soc.13, 472 – 476.

Gromov, M. (1954). Metric structures for Riemannian and Non – Riemannian Spaces.

Lee, G.T. (2018). Abstract algebra: An introductory course. Springer Undergraduate Mathematics Series, Canada. Doi: 10.1007/978 – 3 – 319.

Masaki, M. (2022) “Mean Hausdorff Dimension of some infinite dimensional fractals”2020 Mathematics subject classification.

Monsuru, A.M., Ahmadu, K., and Balla, M. Y. (2020). On the comparative study of compactness and some of its relative notions in Metric and Topological spaces. International Journal of scientific and Research Publication, Vol. 10 Issue 10. 659 – 665.

Murray. (2021). The 54th Spring Topology and Dynamic Conference. Murray State University. USA.

Marc, C. (2009). Volume and Topology.

Morawo, M.A, Danyaro, M.L, Baily, A.S and Azeez, K.Y. (2024) Gromov – Hausdorff Convergence and Topological stability for Actions on Wasserstein Hyperspaces. Journal of Applied Science and Environmental Management. 28(11B). 3815 – 3822.

Morawo, M.A, Azeez, K.Y, Danyaro, M.L, Baily, A. S and Mohammed, A.B. (2024) Comparative Study of Some Topological Properties on Hyperspace of Convex Bodies and Wasserstein hyperspace Associated with Riemannian Manifold. Journal of Applied Science and Environmental Management. 28(12). 4051 – 4056.

Monsuru A Morawo, Mshelia, I. B, Manjak, N.H and Hina, A.D. (2023) Topological properties of some hyperspaces of convex bodies Associated with Riemannian Manifold. International Journal of Advanced in Engineering and Management. 5(3). Pp: 1494 – 1499.

Shanty, N and Raisinganian, M.D. (1965) Element of Real analysis. S. Chand & Company LTD. Ram Nager, New Delhi – 110 055.

Olaf, M. (2021) “Gheeger – Gromov compactness theorem for Manifold with boundary. Adv. Math. 224 – 240.

Olga, G.M., and Peter W.M. (1991). The Riemannian manifold of all Riemannia metrics. Quarterly Oxford Journal of Mathematics 42(183 - 202).

Paige, D. (2022). Hausdorff Dimension and Projection

Willard, S. (2004). General topology. Additson – Wesley.

Zorich, V.A (2004) Mathematical Analysis II. Springer.