Deprecated: preg_replace(): The /e modifier is deprecated, use preg_replace_callback instead in /homepages/31/d279254620/htdocs/clickandbuilds/smf/migrated279797140/Sources/Load.php(225) : runtime-created function on line 3
Proposition 6.4.1: Continuity and Topology
MathCS.org Forums
August 23, 2017, 12:20:01 AM *
Welcome, Guest. Please login or register.

Login with username, password and session length
News: SMF - Just Installed!
 
   Home   Help Search Login Register  
Pages: [1]
  Print  
Author Topic: Proposition 6.4.1: Continuity and Topology  (Read 9805 times)
deepnorth
Newbie
*
Posts: 11


View Profile
« on: August 04, 2009, 11:35:48 AM »

http://www.mathcs.org/analysis/reals/cont/proofs/conttop.html

For the proof (2) => (1).

(2) => (1): Assume that the inverse image f-1(U) of every open set U is open.

Take any point x0 (belong to ) "U" and pick an ε > 0.

Should  it be : take any point x0 (belong to) "D", insteand belong to "U"?
« Last Edit: August 05, 2009, 12:57:49 AM by deepnorth » Logged
webmaster
Administrator
Newbie
*****
Posts: 22


View Profile
« Reply #1 on: August 05, 2009, 02:06:57 PM »

Right, I think it should say: "take any x_0 in D ...", and perhaps somehow the fact that D is open should matter, too, don't you think?
Logged
deepnorth
Newbie
*
Posts: 11


View Profile
« Reply #2 on: August 05, 2009, 10:13:25 PM »

Thanks.
Logged
webmaster
Administrator
Newbie
*****
Posts: 22


View Profile
« Reply #3 on: August 06, 2009, 03:11:59 AM »

Well, thank YOU for helping to fix typos and more serious mistakes - please keep it up!
Logged
Pages: [1]
  Print  
 
Jump to:  

Powered by MySQL Powered by PHP Powered by SMF 1.1.11 | SMF © 2006-2009, Simple Machines LLC Valid XHTML 1.0! Valid CSS!