Actions

Properties of a single space::Local property

::concepts

Locally::space    Group::property    Locally::local    Finite::small    Circle::subgroup    Finitely::spaces

Properties of a single space A topological space is sometimes said to exhibit a property locally if the property is exhibited "near" each point in one of the following different senses:

  1. Each point has a neighborhood exhibiting the property;
  2. Each point has a neighborhood base of sets exhibiting the property.

Sense (2) is in general stronger than sense (1), and caution must be taken to distinguish between the two senses. For example, some variation in the definition of locally compact arises from different senses of the term locally.

Examples


Local property sections
Intro  Properties of a single space  Properties of a pair of spaces  Properties of infinite groups  Properties of finite groups  Properties of commutative rings  

Properties of a single space
PREVIOUS: IntroNEXT: Properties of a pair of spaces
<<>>