# 2008 SpatialConceptsAndRepofSpatialObjs

## 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,

volumeDate ValuetitletypejournaltitleUrldoinoteyear
2008 SpatialConceptsAndRepofSpatialObjsLecture 2 - Spatial Concepts and Representation of Spatial Objectshttp://dbis.ucdavis.edu/courses/ECS266-SQ08/02-concepts.pdf