Dimension Theory

Dimension Theory is a branch of topology that assigns to topological spaces a numerical invariant, called dimension, which quantifies the complexity of the space in terms of the minimal order of refinements of open covers, distinguishing it from other topological invariants by focusing specifically on dimensional properties.

1.6K

Publications

81.5K

Citations

Authors

879

Institutions

Publications per year

2017–2026

165

Parents

Topology

Children

Assouad DimensionCohomological DimensionCovering DimensionDecomposition TheoryDimension Lowering TheoremsDimension Raising TheoremsDimension Theory Of Compact SpacesDimension Theory Of ContinuaDimension Theory Of Function SpacesDimension Theory Of Hyperspaces

Publications

1.6K

Fractal Geometry: Mathematical Foundations and Applications.

K. J. Falconer · Biometrics · 1990 · 6K citations

Natural Sciences, Mathematics, Physics +16

Commutative algebra with a view toward algebraic geometry

Choice Reviews Online · 1996 · 4.2K citations

Natural Sciences, Mathematics, Algebra +14

How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension

Benoît B. Mandelbrot · Science · 1967 · 4.1K citations

Natural Sciences, Oceanography, Coastal Geography +9

Learnability and the Vapnik-Chervonenkis dimension

Anselm Blumer, Andrzej Ehrenfeucht, David Haussler et al. · Journal of the ACM · 1989 · 1.9K citations · Full text

Computing, Computer Science, Mathematics +11

Modern multidimensional scaling : theory and applications

Ingwer Borg, Patrick J. F. Groenen · 1997 · 1.7K citations

Computing, Mathematics, Computational Geometry +16

1–5 of 1.6K

Authors

KJ
K. J. Falconer
University of St Andrews, United Kingdom
17 publications · 7.2K citations
15
h-index
AD
Alexander Dranishnikov
University of Florida, United States
14 publications · 568 citations
13
h-index
KN
Keiô Nagami
Ehime University, Japan
10 publications · 152 citations
10
h-index
JA
Juan A. Rodríguez‐Velázquez
Universitat Rovira i Virgili, Spain
9 publications · 343 citations
9
h-index
JM
Jonathan M. Fraser
University of St Andrews, United Kingdom
9 publications · 362 citations
9
h-index

1–5 of 2K

Institutions

879

1–8 of 879

Venues

Transactions of the American Mathematical Society
TRAN · 76 publications · 3.3K citations
29
h-index
Proceedings of the American Mathematical Society
PROC · 74 publications · 2.2K citations
27
h-index
Pacific Journal of Mathematics
39 publications · 1.5K citations
25
h-index
Communications in Algebra
58 publications · 1.7K citations
24
h-index
Mathematical Proceedings of the Cambridge Philosophical Society
33 publications · 1.6K citations
19
h-index

1–5