Minimal Totally Disconnected Spaces
... ABSTRACT. 7)-minimal and 7)-closed spaces are studied for the cases: 7) is totally disconnected and Hausdorff; and 7) is totally separated. Several characterization, embedding and product theorems are obtained, and some examples are given. ...
... ABSTRACT. 7)-minimal and 7)-closed spaces are studied for the cases: 7) is totally disconnected and Hausdorff; and 7) is totally separated. Several characterization, embedding and product theorems are obtained, and some examples are given. ...
A CROSS SECTION THEOREM AND AN APPLICATION TO C
... to B, is open, tt(B) = J, and yet there is no Borel cross section (in this case, there is no Borel uniformization). Recall that if F is a subset of A" X Y, then a uniformization of F is a subset F of E such that Ex ^= 0 if and only if Fx consists of exactly one point, where Ex = [y\(x, y) is in E]. ...
... to B, is open, tt(B) = J, and yet there is no Borel cross section (in this case, there is no Borel uniformization). Recall that if F is a subset of A" X Y, then a uniformization of F is a subset F of E such that Ex ^= 0 if and only if Fx consists of exactly one point, where Ex = [y\(x, y) is in E]. ...
Scott Topology and its Relation to the Alexandroff Topology
... [13]. These problems also have increased the interaction between topology and related areas of mathematics such as order theory and topological algebra [13] [Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of ordering, providin ...
... [13]. These problems also have increased the interaction between topology and related areas of mathematics such as order theory and topological algebra [13] [Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of ordering, providin ...
Fascicule
... We emphasize that when we talk of a limit closed subcategory B ⊆ C , we mean not only that B is complete, but also that the limits in B are the same as in those of C , that is, that the inclusion B ⊆ C preserves limits. The limit closure of B is the meet of all limit closed subcategories of C that c ...
... We emphasize that when we talk of a limit closed subcategory B ⊆ C , we mean not only that B is complete, but also that the limits in B are the same as in those of C , that is, that the inclusion B ⊆ C preserves limits. The limit closure of B is the meet of all limit closed subcategories of C that c ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.