local contractibility, cell-like maps, and dimension
... a continuous surjection /: X -» Y between compact spaces is called cell-like provided that f~l(y) has trivial shape for every y e Y. One of the most outstanding open problems in geometric topology is whether a cell-like map of a compactum can raise dimension. This problem is known as the "cell-like ...
... a continuous surjection /: X -» Y between compact spaces is called cell-like provided that f~l(y) has trivial shape for every y e Y. One of the most outstanding open problems in geometric topology is whether a cell-like map of a compactum can raise dimension. This problem is known as the "cell-like ...
Unitary Group Actions and Hilbertian Polish
... We now turn to the unitary group U∞ . We first recall some notation and basic facts about the Hilbert space H and its unitary group U (H). A linear operator T : H → H is unitary if hT u, T vi = hu, vi, for all u, v ∈ H. The group operation of U (H) is the composition of unitary operators. The above ...
... We now turn to the unitary group U∞ . We first recall some notation and basic facts about the Hilbert space H and its unitary group U (H). A linear operator T : H → H is unitary if hT u, T vi = hu, vi, for all u, v ∈ H. The group operation of U (H) is the composition of unitary operators. The above ...
On some locally closed sets and spaces in Ideal Topological
... Definition 2.3. A topological space (X, ) is said to be T½-space [5] if every g-closed set in it is closed. Definition 2.4. Let (X, , I) be an ideal space. A subset A is said to be (i) Ig-closed [3] if A* U whenever AU and U is open. (ii) Ig-locally *-closed [7] if there exist an Ig-open set U a ...
... Definition 2.3. A topological space (X, ) is said to be T½-space [5] if every g-closed set in it is closed. Definition 2.4. Let (X, , I) be an ideal space. A subset A is said to be (i) Ig-closed [3] if A* U whenever AU and U is open. (ii) Ig-locally *-closed [7] if there exist an Ig-open set U a ...
2. Direct and inverse images.
... (2.11) Example. Even when the homomorphism u : F → G is a homomorphism of sheaves the presheaf H of Section (2.?) does not have to be a sheaf. Let X = {x0 , x1 , x2 } be the topological space with open sets ∅, X, U0 = {x0 }, U1 = {x0 , x1 }, U2 = {x0 , x2 }. The constant presheaf F on X with fiber Z ...
... (2.11) Example. Even when the homomorphism u : F → G is a homomorphism of sheaves the presheaf H of Section (2.?) does not have to be a sheaf. Let X = {x0 , x1 , x2 } be the topological space with open sets ∅, X, U0 = {x0 }, U1 = {x0 , x1 }, U2 = {x0 , x2 }. The constant presheaf F on X with fiber Z ...
