Science Explorer Back to mapMap
Discussion
Topic · Geometry and Topology

Advanced Topology and Set Theory

Advanced Topology and Set Theory is a research topic within Geometry and Topology. Science Explorer counts 20k research works in it since 1950. 10.0% of them reached the world's top 10% most cited for their field and year.

This cluster of papers covers topics in model theory, topological dynamics, and their applications to homogeneous structures, o-minimal structures, large cardinals, and forcing axioms. It explores the interactions between abstract elementary classes, definable sets, and automorphism groups, with connections to Ramsey theory and the structure of compact groups.

  • Model Theory
  • Topological Dynamics
  • Homogeneous Structures
  • O-Minimal Structures
  • Large Cardinals
  • Forcing Axioms
  • Abstract Elementary Classes
  • Definable Sets
  • Automorphism Groups
  • Ramsey Theory
Research works
20k
fractional, since 1950
In the world top 10%
2k
per year above
Top-10% rate
10.0%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+7%
the tick is no change
Largest producer
United States
29% of the 10 largest, 2022-now
Advanced Topology and Set Theory

Which countries lead Advanced Topology and Set Theory research?

By volume, the United States and China publish the most (406 and 239 works in 2022-now).

By volume, 2022-now

  1. 1 United States 406 works
  2. 2 China 239 works
  3. 3 Russia 131 works
  4. 4 India 105 works
  5. 5 France 104 works
  6. 6 Poland 96 works
  7. 7 United Kingdom 95 works
  8. 8 Germany 88 works
  9. 9 Japan 77 works
  10. 10 Italy 75 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 28.7%China: 16.9%Russia: 9.3%India: 7.4%6 others listed: 37.8%29%largest
United States406 · 28.7%China239 · 16.9%Russia131 · 9.3%India105 · 7.4%6 others listed535 · 37.8%

Shares of the rows listed above, not of the whole node.

Which institutions lead Advanced Topology and Set Theory research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Topology and Set Theory research, followed by Russian Academy of Sciences and Lomonosov Moscow State University.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 53 works
  2. 2 Russian Academy of SciencesRussia 33 works
  3. 3 Lomonosov Moscow State UniversityRussia 26 works
  4. 4 Polish Academy of SciencesPoland 21 works
  5. 5 Universidad Nacional Autónoma de MéxicoMexico 21 works
  6. 6 Czech Academy of SciencesCzechia 20 works
  7. 7 University of ViennaAustria 19 works
  8. 8 TU WienAustria 17 works
  9. 9 Hebrew University of JerusalemIsrael 17 works
  10. 10 Charles UniversityCzechia 16 works

Who are the leading researchers in Advanced Topology and Set Theory?

The most-cited researchers publishing on Advanced Topology and Set Theory include R. W. L. Jones, Hywel C Williams and Guanrong Chen.

  1. 1 R. W. L. Jones United Kingdom 189k citations
  2. 2 Hywel C Williams United Kingdom 126k citations
  3. 3 Guanrong Chen China 116k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Advanced Topology and Set Theory?

The most cited paper in Advanced Topology and Set Theory is "Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)" (Michael Gromov, 1981), with 1,846 citations. Next come "An Introduction to Harmonic Analysis." (1,713) and "Measures on the Closed Subspaces of a Hilbert Space" (1,020).

Most cited papers
#PaperReleasedCitations
1 Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits) Michael Gromov · Publications mathématiques de l IHÉS 7 Dec 1981 1,846
2 An Introduction to Harmonic Analysis. Guido Weiss, Yitzhak Katznelson · American Mathematical Monthly Apr 1970 1,713
3 Measures on the Closed Subspaces of a Hilbert Space Andrew M. Gleason Book chapter 1975 1,020
4 A Decomposition Theorem for Partially Ordered Sets R. P. Dilworth · Birkhäuser Boston eBooks Book chapter 2009 1,009
5 Convergence of convex sets and of solutions of variational inequalities Umberto Mosco · Advances in Mathematics Open access Oct 1969 988
All 100 most cited papers, with filters and sorting

Where is Advanced Topology and Set Theory research done?

The largest centres of Advanced Topology and Set Theory research in 2022-now are Moscow (Russia), Paris (France), Vienna (Austria) and Prague (Czechia).

Largest cities, 2022-now

  1. 1 MoscowRussia 65 works
  2. 2 ParisFrance 42 works
  3. 3 ViennaAustria 40 works
  4. 4 PragueCzechia 38 works
  5. 5 Mexico CityMexico 38 works
  6. 6 BeijingChina 30 works
  7. 7 WarsawPoland 29 works
  8. 8 BudapestHungary 28 works
  9. 9 New YorkUnited States 21 works
  10. 10 NanjingChina 20 works
See Advanced Topology and Set Theory on the map

Where is the best place to study Advanced Topology and Set Theory?

Among universities, judged by research, Lomonosov Moscow State University, Hebrew University of Jerusalem and University of California, Berkeley score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%mean 11.57%fractional works in this field (log) →share of work in the world top 10% →University of OxfordHebrew University of…Lomonosov Moscow Sta…University of Califo…
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Lomonosov Moscow State UniversityRussia 80.714.6%15.5×26 +46.6%
2Hebrew University of JerusalemIsrael 77.014.7%16.4×17 -5.2%
3University of California, BerkeleyUnited States 70.76.2%8.0×15 +104.5%
4University of OxfordUnited Kingdom 64.915.4%4.4×12 +91.9%
5University of ViennaAustria 63.56.7%19.3×19 +21.2%
6TU WienAustria 58.25.8%28.2×17 +88.9%
7University of California San DiegoUnited States 56.718.0%4.4×8 +103.3%
8Tel Aviv UniversityIsrael 56.013.0%5.9×9 -18.1%
9City University of New YorkUnited States 55.510.5%12.8×14 +28.8%
10Charles UniversityCzechia 54.110.8%17.5×16 -19.2%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Advanced Topology and Set Theory, country by country

Is Advanced Topology and Set Theory research growing?

Output in 2022-2025 was 7% higher than in 2018-2021, peaking in 2023. The fastest-growing topics are Advanced Topology and Set Theory.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Advanced Topology and Set Theory as a percentage of every work published that year, 0.0087% in 2024.

still counting0.050%0.10%Advanced Topology and Set Theory0.0085% in 202519801990200020102020

Fractional works of Advanced Topology and Set Theory over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Advanced Topology and Set Theory10.2% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

Discussion

Ask a question or share a note about Advanced Topology and Set Theory. Posts are plain text and can be reported.