Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 31st 2012
   • (edited Aug 31st 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI tried to prettify the entry _[[topological space]]_ a bit more: * made an attempt at adding an [Idea-section](http://ncatlab.org/nlab/show/topological+space#Idea) (feel free to work on that, it's just a quick idea motivated more from the desire to have such a section at all than from an attempt to do it any justice). * collected the three Definition-sections to subsections of a single [Definition-section](http://ncatlab.org/nlab/show/topological+space#Definitions) * polished and expanded the [Standard definition section](#http://ncatlab.org/nlab/show/topological+space#StandardDefinition).

   I tried to prettify the entry topological space a bit more:

   • made an attempt at adding an Idea-section (feel free to work on that, it’s just a quick idea motivated more from the desire to have such a section at all than from an attempt to do it any justice).

   • collected the three Definition-sections to subsections of a single Definition-section

   • polished and expanded the Standard definition section.

2. • CommentRowNumber2.
   • CommentAuthormdiamond
   • CommentTimeApr 25th 2020
   • PermaLink
   Author: mdiamond
   Format: TextCould someone clarify what the word "respond" means in the context of the [[topological space]] entry? The text explains topological equivalence by referring to the way a space "responds" to open intervals. I realize that our definitions of words have to bottom-out somewhere, but I feel like clarifying the meaning of this word would help me (and possibly others) to grasp the fundamental essence of topological spaces and what "topological equivalence" means. Is there a technical way to describe what it denotes here?

   Could someone clarify what the word "respond" means in the context of the topological space entry? The text explains topological equivalence by referring to the way a space "responds" to open intervals. I realize that our definitions of words have to bottom-out somewhere, but I feel like clarifying the meaning of this word would help me (and possibly others) to grasp the fundamental essence of topological spaces and what "topological equivalence" means. Is there a technical way to describe what it denotes here?