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In mathematics, the subspace theorem says that points of small height in projective space lie in a finite number of hyperplanes. It is a result obtained by Wolfgang M. Schmidt (1972).
The analysis highlights Applications, Statement and Overview as prominent areas in the source structure around Subspace theorem.
Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.
Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
The extracted context around Subspace theorem shows recurring relationship patterns in the source. For example, Subspace theorem → Dirichlet's, If, One, Roth, Siegel, The, Thue Another extracted example is Subspace theorem → L1, Ln, Qn, The. Use these groups to spot repeated connection types before inspecting the individual relationships.
Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
theorem diophantine mr number schmidt doi mathematics wolfgang equations 10 subspace points isbn zbl approximation 1972 form vol lie finite
TTTA extracted 13 structured relationships around Subspace theorem. Examples in this analysis include Siegel's theorem on integral points → instance of → ApplicationsThe theorem may be used to obtain results on Diophantine equations and Subspace theorem → related to A corollary on Diophantine approximation → The. The table shows each extracted connection, where it came from and its confidence.
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Siegel's theorem on integral points | instance of | ApplicationsThe theorem may be used to obtain results on Diophantine equations | 0.80 | text |
| solution of the S-unit equation.A corollary on Diophantine approximationThe following corollary to the subspace theorem is often itself referred to as the subspace theorem | instance of | ApplicationsThe theorem may be used to obtain results on Diophantine equations | 0.80 | text |
| Subspace theorem | related to A corollary on Diophantine approximation | The | 0.60 | section |
| Subspace theorem | related to A corollary on Diophantine approximation | If | 0.60 | section |
| Subspace theorem | related to A corollary on Diophantine approximation | Thue | 0.60 | section |
| Subspace theorem | related to A corollary on Diophantine approximation | Siegel | 0.60 | section |
| Subspace theorem | related to A corollary on Diophantine approximation | Roth | 0.60 | section |
| Subspace theorem | related to A corollary on Diophantine approximation | One | 0.60 | section |
| Subspace theorem | related to A corollary on Diophantine approximation | Dirichlet's | 0.60 | section |
| Subspace theorem | related to Statement | The | 0.60 | section |
| Subspace theorem | related to Statement | L1 | 0.60 | section |
| Subspace theorem | related to Statement | Ln | 0.60 | section |
The concept neighborhoods around Subspace theorem bring nearby vocabulary together. In this analysis, examples include Corollary, Points and Subspace. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
For Subspace theorem, one of the stronger structural bridges in this analysis connects Subspace theorem with Statement. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
TTTA analyzes the structure around Subspace theorem to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Applications, Statement & Overview, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
Source: Wikipedia — Subspace theorem · EN edition · Analysis: TopicsToTalkAbout