Classifying Spaces - School of Mathematics and Statistics
... Theorem 4.1 A principal G-bundle π : E −→ B, with G and B having the homotopy type of a CW-complex, is universal if and only if E is contractible. Corollary 4.1 Let G be a topological group. Then BG is path-connected. ...
... Theorem 4.1 A principal G-bundle π : E −→ B, with G and B having the homotopy type of a CW-complex, is universal if and only if E is contractible. Corollary 4.1 Let G be a topological group. Then BG is path-connected. ...
ON DOUBLE-DERIVED SETS IN TOPOLOGICAL SPACES In [1
... subset of X, then clearly none of the iterated derived sets of A is closed. In view of these remarks, the question of A.Lelek seems to be natural. The answer is a consequence of the following theorem which characterizes topological spaces in which there is a subset with non-closed double derived set ...
... subset of X, then clearly none of the iterated derived sets of A is closed. In view of these remarks, the question of A.Lelek seems to be natural. The answer is a consequence of the following theorem which characterizes topological spaces in which there is a subset with non-closed double derived set ...
PH Kropholler Olympia Talelli
... Proposition. Let G be a group. Then there is a ii?G-module I such that (i) I is free as a z F-module for each finite subgroup F of G, (ii) H’(G, I) # 0. In fact it is easy to deduce the following more general result of which Theorem 1 is a special case. Theorem 2. Let G be a group which acts simpkia ...
... Proposition. Let G be a group. Then there is a ii?G-module I such that (i) I is free as a z F-module for each finite subgroup F of G, (ii) H’(G, I) # 0. In fact it is easy to deduce the following more general result of which Theorem 1 is a special case. Theorem 2. Let G be a group which acts simpkia ...
1 - ckw
... 20. Let (S,T1) & (S,T2) be 2 topological spaces. T1 is weaker than T2 if every member of T1 belongs to T2. T1 is then coarser than T2 & T2 is finer (stronger) than T1. 21. Topology of Minkowski space is not known. One choice is the Zeeman topology: the finest topology on R4 which induces an E3 topol ...
... 20. Let (S,T1) & (S,T2) be 2 topological spaces. T1 is weaker than T2 if every member of T1 belongs to T2. T1 is then coarser than T2 & T2 is finer (stronger) than T1. 21. Topology of Minkowski space is not known. One choice is the Zeeman topology: the finest topology on R4 which induces an E3 topol ...