Minimal Totally Disconnected Spaces
... easyto verify that G is a filter basewith a uniqueadherentpoint (namely p). The fact that .Y is free impliesthat G is nonconvergent, and that p is its onlyadherentpoint. We showthat • is a P-filter base.Let C C X • {p} be any nondegenerate set. There exist (disjoint)opensetsL and M of X which separa ...
... easyto verify that G is a filter basewith a uniqueadherentpoint (namely p). The fact that .Y is free impliesthat G is nonconvergent, and that p is its onlyadherentpoint. We showthat • is a P-filter base.Let C C X • {p} be any nondegenerate set. There exist (disjoint)opensetsL and M of X which separa ...
MAPPING STACKS OF TOPOLOGICAL STACKS Contents 1
... 2.3. Hurewicz topological stacks. One drawback of the 2-category of topological stacks is that homotopy between maps of topological stacks is not in general an equivalence relation (because it may not be transitive). More precisely, homotopies between maps (with target X a topological stack) do not ...
... 2.3. Hurewicz topological stacks. One drawback of the 2-category of topological stacks is that homotopy between maps of topological stacks is not in general an equivalence relation (because it may not be transitive). More precisely, homotopies between maps (with target X a topological stack) do not ...
T A G Coarse homology theories
... We can form the category of all coarse spaces and coarse maps. We call this category the coarse category. We call a coarse map f : X ! Y a coarse equivalence if there is a coarse map g : Y ! X such that the composites g f and f g are close to the identities 1X and 1Y respectively. Let X and Y be ...
... We can form the category of all coarse spaces and coarse maps. We call this category the coarse category. We call a coarse map f : X ! Y a coarse equivalence if there is a coarse map g : Y ! X such that the composites g f and f g are close to the identities 1X and 1Y respectively. Let X and Y be ...
FELL TOPOLOGY ON HYPERSPACES OF LOCALLY COMPACT
... It is clear that the Fell topology is weaker than the Vietoris one. On the other hand, these two topologies coincide if X is compact. In case of locally compact noncompact space X the Fell topology on Cld∗ (X) is a bit better than the Vietoris topology since the former topology always is compact [Fe ...
... It is clear that the Fell topology is weaker than the Vietoris one. On the other hand, these two topologies coincide if X is compact. In case of locally compact noncompact space X the Fell topology on Cld∗ (X) is a bit better than the Vietoris topology since the former topology always is compact [Fe ...
Summary of Objectives
... Obj: Apply theorems about inequalities in triangles. (The sum of any two sides of a triangle is greater than the third. If two sides of a triangle are unequal, then the larger angle lies opposite the longer side. If two angles of a triangle are unequal, then the longer side lies opposite the larger ...
... Obj: Apply theorems about inequalities in triangles. (The sum of any two sides of a triangle is greater than the third. If two sides of a triangle are unequal, then the larger angle lies opposite the longer side. If two angles of a triangle are unequal, then the longer side lies opposite the larger ...
