Mathematics Branches, Topics, and Sub-Topics

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51Gxx Topological and differential geometry (synthetic aspects)

This subtopic introduces the core ideas in topological and differential geometry (synthetic aspects), including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

51G05 Ordered geometries (ordered incidence structures, etc.)

Overview

Ordered geometries add a notion of order or betweenness to incidence structures, connecting geometry with order theory.

Related Wikipedia Page

Wikipedia: Order theory

Useful Links

Key Ideas

  • betweenness
  • order relations
  • ordered incidence

Typical Uses

Useful for understanding geometries with orientation, convexity, or order-based axioms.

Applications

  • Ordered structures
  • Convex geometry
  • Foundations of geometry

References

Recommended Textbooks