The Emergence Machine

Topology

abstract · Mathematics · Level 5 · E0

E0Spacetime

Each concept here is mapped to its prerequisites — the ideas you'd need first to understand it — all the way down to four foundations: Space, Time, Energy, Pattern. Click any prerequisite to drill down, or scroll for the chain graph.

Trace. Question. Emerge.

Emergence definition

Topology studies the properties that remain unchanged under continuous transformations, building upon the organized arrangement of matter and the mathematics of geometry that govern its transformations.

Compare Topology with…

Wiktionary senses

External reference — all senses of the word “topology” on Wiktionary. This atlas concept maps to only the slice of meaning relevant to the prerequisite graph.

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Source: Wiktionary — “topology”. Content available under CC BY-SA 4.0.

Historical origin

Origin word
topos+logos
Origin language
grc

Prerequisite chain

Possible path of this concept down to the fundamental substrate.

thisfoundationsL5L4L3L2L1L0TopologyGeometryShapeFormStructureMatterEnergyPatternSpaceE1 concrete → E14 abstract

Neighborhood

Direct prerequisites above, concepts that depend on this one below.

used byprerequisitesHilberts Sixteen…L6TopologyL5StructureL2GeometryL4E1 concrete → E14 abstract

In other languages

Prerequisites

What you need to understand first.

  • Structure L2 (requires) architecture sense
    Understanding structure is essential for grasping topology
  • Geometry L4 (requires)
    Topology is a branch of geometry studying properties that remain unchanged under continuous transformations.

Used by