PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (236)
Orphanage
Unclass'd (1)
Unproven (540)
Corrections (51)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Copyright
About
Owner confidence rating: High Entry average rating: High
Polish space (Definition)

A Polish space is a topological space that is homeomorphic to some complete separable metric space.

Equivalently, a topological space is a Polish space if it is separable and completely metrizable.

Examples of Polish spaces are the euclidean space $\mathbb{R}^n$ (with the usual topology), the Cantor space, and the Baire space.



"Polish space" is owned by Koro.
(view preamble | get metadata)

View style:

See Also: topological G-space, Polish group, categories of Polish groups and Polish spaces, spaces homeomorphic to Baire space


Attachments:
Polish spaces up to Borel isomorphism (Theorem) by gel
Log in to rate this entry.
(view current ratings)

Cross-references: Cantor space, usual topology, Euclidean space, completely metrizable, metric space, separable, complete, homeomorphic, topological space
There are 26 references to this entry.

This is version 2 of Polish space, born on 2005-01-31, modified 2007-11-30.
Object id is 6693, canonical name is PolishSpace.
Accessed 3679 times total.

Classification:
AMS MSC: 54E50 (General topology :: Spaces with richer structures :: Complete metric spaces)
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)