My Math Forum Is there a topological space with fundamental group that does not contain anything?

 Topology Topology Math Forum

 August 9th, 2015, 02:09 AM #1 Newbie   Joined: Aug 2015 From: Italy Posts: 5 Thanks: 0 Is there a topological space with fundamental group that does not contain anything? Is there a topological space with fundamental group that does not contain anything? If G is a group $\displaystyle G \not = \emptyset$, and $\displaystyle e \in G$ where $\displaystyle e$ is identity element, so I think that does not exist. Is it correct? Thanks in advance. Last edited by skipjack; August 9th, 2015 at 07:01 AM.
 August 9th, 2015, 05:34 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 ??? The "fundamental group" of a topological space is, first of all, a group! Every group has to contain at least an identity so the "fundamental group" must contain at least the identity.
 August 9th, 2015, 06:52 AM #3 Newbie   Joined: Aug 2015 From: Italy Posts: 5 Thanks: 0 Yes, this is what I meant too. Thanks
September 8th, 2015, 03:52 PM   #4
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

Quote:
 Originally Posted by Country Boy ??? The "fundamental group" of a topological space is, first of all, a group! Every group has to contain at least an identity so the "fundamental group" must contain at least the identity.
Added: The "fundamental group" of a topological space is the set of all homeomorphisms from the space to itself with composition of functions as operation. That always includes the identity map as its identity element.

 Tags fundamental, group, space, topological

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post fairyrak Real Analysis 5 December 30th, 2011 05:39 PM eraldcoil Abstract Algebra 4 March 28th, 2011 08:55 PM TTB3 Real Analysis 2 April 19th, 2009 08:52 AM mingcai6172 Real Analysis 0 March 21st, 2009 02:35 PM Thomas Keyes Real Analysis 1 November 24th, 2007 11:04 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top