Topology (disambiguation)

Topology, the study of surfaces, is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these properties are the topological invariants.

Topology may also refer to:

• Topology, the collection of open sets used to define a topological space
• Lawvere–Tierney topology of a topos
• Grothendieck topology of a category
• Topology (journal), a mathematical journal, with an emphasis on subject areas related to topology and geometry
• Spatial effects that cannot be described by topography, i.e., social, economical, spatial, or phenomenological interactions
• The specific orientation of transmembrane proteins.
• Topology (electronics), a configuration of electronic components.
• Network topology, configurations of computer or biological networks.
• Topology (musical ensemble), an Australian post-classical quintet
• Geospatial topology, the study or science of places with applications in earth science, geography, human geography, and geomorphology.
  • In geographic information systems and their data structures, topology and planar enforcement are the storing of a border line between two neighboring areas (and the border point between two connecting lines) only once. Thus, any rounding errors might move the border, but will not lead to gaps or overlaps between the areas.
  • Also in cartography, a topological map is a greatly simplified map that preserves the mathematical topology while sacrificing scale and shape
  • Topology is often confused with the geographic meaning of topography (originally the study of places). The confusion may be a factor in topographies having become confused with terrain or relief, such that they are essentially synonymous.
• In phylogenetics, the branching pattern of a phylogenetic tree.
• TopologiLinux, a Linux distribution