discrete topology of cardinality 6

Theorem 1.15 shows that for any cardinal number m and any metrizable space X seven conditions are equivalent.
Included in these seven are the following:

(a) every (closed) discrete subspace of X has cardinality less than or equal to m;
(b) X has a dense subset of cardinality less than or equal to m.

These conditions may be formulated in an arbitrary topological space and we consider how they are related in such a wider setting.

Active Rosters
Active Rosters
Active roster for discrete topology of cardinality 6 playing in Intermediate for ozfortress season 32
  • donna
  • Ravu4
  • Voltage captain
  • Pengstah
  • tokahontas
  • moomoo
  • bubsdoge
  • helenaaa
  • verty
  • Tissueman
    • League Points 12
    League Rank #7
    Seed #4
    Rounds Won 6
    Rounds Lost 8
    Rounds Drawn 0
    Points Scored 33.0
    Points Scored Difference -1.0
    Bye Matches 0
  • Tissueman joined the team on Sat Nov 20 19:55:25 2021
  • verty joined the team on Mon Nov 8 23:22:27 2021
  • adam left the team on Thu Oct 7 22:20:55 2021
  • helenaaa joined the team on Thu Oct 7 14:38:46 2021
  • bubsdoge joined the team on Wed Oct 6 22:37:47 2021
  • adam joined the team on Wed Oct 6 22:37:47 2021
  • moomoo joined the team on Wed Oct 6 22:37:47 2021
  • tokahontas joined the team on Wed Oct 6 22:37:47 2021
  • Pengstah joined the team on Wed Oct 6 22:37:47 2021
  • Voltage joined the team on Wed Oct 6 22:37:47 2021
  • Ravu4 joined the team on Wed Oct 6 22:37:47 2021
  • donna joined the team on Wed Oct 6 22:37:47 2021
    • Past Rosters
    Last & Found placed 10th in Division 2 for ozfortress winter league 2021
  • donna
  • Ravu4
  • Voltage captain
  • Pengstah
  • Jol
  • tokahontas
  • moomoo
  • kory
  • adam
  • a team of ants in their prime League Administrator
    • Round Home Team vs Away Team
    #1 Ascension
    5 : 1
    4 : 1
    0 : 0
    		 Last & Found Match Page
    #2 smarty cats
    7 : 4
    4 : 3
    0 : 0
    		 Last & Found Match Page
    #3 Last & Found
    0 : 3
    2 : 6
    0 : 0
    		 shoegaze haters Match Page
    League Points 0
    League Rank #10
    Seed #10
    Rounds Won 0
    Rounds Lost 6
    Rounds Drawn 3
    Points Scored 11.0
    Points Scored Difference -18.0
    Bye Matches 0
  • a team of ants in their prime joined the team on Thu Aug 12 15:06:54 2021
  • adam joined the team on Thu Aug 12 15:06:54 2021
  • kory joined the team on Thu Aug 12 15:06:54 2021
  • moomoo joined the team on Thu Aug 12 15:06:54 2021
  • tokahontas joined the team on Thu Aug 12 15:06:54 2021
  • Jol joined the team on Thu Aug 12 15:06:54 2021
  • Pengstah joined the team on Thu Aug 12 15:06:54 2021
  • Voltage joined the team on Thu Aug 12 15:06:54 2021
  • Ravu4 joined the team on Thu Aug 12 15:06:54 2021
  • donna joined the team on Thu Aug 12 15:06:54 2021
    • punoɟ puɐ ʇsɐl placed 6th in Intermediate for ozfortress Autumn Cup 2021
  • Ravu4
  • Voltage captain
  • Pengstah
  • Jol
  • tokahontas
  • moomoo
  • cuin lumby
    • League Points 8
    League Rank #6
    Seed #1
    Rounds Won 2
    Rounds Lost 2
    Rounds Drawn 0
    Points Scored 9.0
    Points Scored Difference -1.0
    Bye Matches 0
  • cuin lumby joined the team on Thu Apr 22 17:54:43 2021
  • moomoo joined the team on Thu Apr 22 17:54:43 2021
  • tokahontas joined the team on Thu Apr 22 17:54:43 2021
  • Jol joined the team on Thu Apr 22 17:54:43 2021
  • Pengstah joined the team on Thu Apr 22 17:54:43 2021
  • Voltage joined the team on Thu Apr 22 17:54:43 2021
  • Ravu4 joined the team on Thu Apr 22 17:54:43 2021
    • Last & Found placed 3rd in Main for ozfortress season 30
  • kory
  • donna
  • Ravu4
  • Voltage captain
  • Pengstah
  • Jol
  • moomoo
  • olaf
  • tokahontas
  • b1
    • League Points 22
    League Rank #3
    Seed #4
    Rounds Won 11
    Rounds Lost 7
    Rounds Drawn 0
    Points Scored 55.0
    Points Scored Difference 14.0
    Bye Matches 0
  • b1 joined the team on Sat Mar 13 20:07:24 2021
  • Doctrine left the team on Fri Feb 26 20:05:02 2021
  • tokahontas joined the team on Sat Feb 13 19:20:32 2021
  • olaf joined the team on Sat Feb 13 19:20:30 2021
  • moomoo joined the team on Sat Feb 13 19:20:27 2021
  • Doctrine joined the team on Wed Jan 27 23:48:06 2021
  • Jol joined the team on Wed Jan 27 23:48:06 2021
  • Pengstah joined the team on Wed Jan 27 23:48:06 2021
  • Voltage joined the team on Wed Jan 27 23:48:06 2021
  • Ravu4 joined the team on Wed Jan 27 23:48:06 2021
  • donna joined the team on Wed Jan 27 23:48:06 2021
  • kory joined the team on Wed Jan 27 23:48:06 2021
    • Transfer History
    • Tissueman joined the team on Thu Nov 11 19:18:21 2021
    • verty joined the team on Sat Oct 23 23:15:36 2021
    • helenaaa joined the team on Thu Oct 7 09:49:27 2021
    • adam left the team on Thu Oct 7 01:19:59 2021
    • kory left the team on Thu Oct 7 00:15:49 2021
    • olaf left the team on Wed Oct 6 10:26:22 2021
    • b1 left the team on Wed Oct 6 10:26:14 2021
    • bubsdoge joined the team on Mon Oct 4 00:15:00 2021
    • a team of ants in their prime joined the team on Thu Aug 12 15:06:03 2021
    • adam joined the team on Thu Aug 12 12:00:20 2021
    • kory joined the team on Wed Aug 11 22:47:14 2021
    • tiMe joined the team on Tue Jul 20 17:38:36 2021
    • kory left the team on Sun May 16 22:30:20 2021
    • cuin lumby joined the team on Thu Apr 22 17:29:26 2021
    • b1 joined the team on Wed Mar 10 23:05:50 2021
    • Doctrine left the team on Thu Feb 25 00:06:06 2021
    • moomoo joined the team on Thu Feb 4 21:52:52 2021
    • olaf joined the team on Thu Feb 4 21:13:04 2021
    • tokahontas joined the team on Wed Feb 3 23:06:28 2021
    • Doctrine joined the team on Tue Jan 26 22:46:39 2021
    • Jol joined the team on Tue Jan 26 22:16:01 2021
    • Pengstah joined the team on Tue Jan 26 21:06:40 2021
    • Voltage joined the team on Tue Jan 26 16:23:37 2021
    • Ravu4 joined the team on Tue Jan 26 15:20:20 2021
    • donna joined the team on Tue Jan 26 11:49:46 2021
    • kory joined the team on Tue Jan 26 05:13:20 2021
    External Links