2008 SpatialConceptsAndRepofSpatialObjs

• (Gertz, 2008) ⇒ Michael Gertz. (2008). “Lecture 2 - Spatial Concepts and Representation of Spatial Objects ECS 266 – Spatial Databases, UC Davis.

Subject Headings: Topology, Spatial Database

Notes

• It contains proposed definitions for: Topology, Topology Space, …

Quotes

Topology

• Branch of mathematics that deals with spatial relationships that are preserved under bicontinuous deformation (stretching without tearing or gluing), sometimes called rubber-sheet geometry.
• The idea is that some geometric problems do not depend on the exact shape of objects involved, but rather on the way objects are “connected to each other”
• Spaces studied in topology are called topological spaces.
• Elementary topology is often called point-set topology

Topological Space

• (Def) A topological space is a set X of elements, called points, with a collection T of subsets of X, called open sets, that satisfy the following three axioms:
  • [A1] The empty set and X are in T.
  • [A2] The union of any collection of sets in T is also in T.
  • [A3] The intersection of any pair of sets in T is also in T,

	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2008 SpatialConceptsAndRepofSpatialObjs	Michael Gertz			Lecture 2 - Spatial Concepts and Representation of Spatial Objects			http://dbis.ucdavis.edu/courses/ECS266-SQ08/02-concepts.pdf