Topologies on the set of closed subsets
... internal subset of *X, let St (A) = {x E X \ μ (x) Π A ^ 0}. Under suitable conditions on *X St(A) is always closed. Now, if A, BE*X, Narens defines A ~ B provided St(A) = St(B). He uses this relationship to define a topology which he calls the compact topology. In the present paper we will call thi ...
... internal subset of *X, let St (A) = {x E X \ μ (x) Π A ^ 0}. Under suitable conditions on *X St(A) is always closed. Now, if A, BE*X, Narens defines A ~ B provided St(A) = St(B). He uses this relationship to define a topology which he calls the compact topology. In the present paper we will call thi ...
Lecture 4: examples of topological spaces, coarser and finer
... If U satisfies either of these equivalent conditions, we call it B-open. Now by the definition I gave earlier, an open subset of R is one which is BR -open, where BR is the set of open intervals. Warning 10. If anyone’s taken linear algebra, this is a good time to remark that the usage of the word “ ...
... If U satisfies either of these equivalent conditions, we call it B-open. Now by the definition I gave earlier, an open subset of R is one which is BR -open, where BR is the set of open intervals. Warning 10. If anyone’s taken linear algebra, this is a good time to remark that the usage of the word “ ...
Homogeneous Plane Continua
... plane continua.Using these results,we prove that every decomposablesubcontinuum of a homogeneous indecomposable planecontinuumcontainsa homogeneous indecomposable continuum.It follows that Bing's theorem remains true if the word "arc" is replaced by "hereditarilydecomposable continuum." ...
... plane continua.Using these results,we prove that every decomposablesubcontinuum of a homogeneous indecomposable planecontinuumcontainsa homogeneous indecomposable continuum.It follows that Bing's theorem remains true if the word "arc" is replaced by "hereditarilydecomposable continuum." ...
Unitary Group Actions and Hilbertian Polish
... of actions, but faithfulness is still a significant concept because of its pertinence to the Topological Vaught Conjecture. We will elaborate on the details in the text and give definitions as they become relevant. As an important application we also identify a natural equivalence relation that is o ...
... of actions, but faithfulness is still a significant concept because of its pertinence to the Topological Vaught Conjecture. We will elaborate on the details in the text and give definitions as they become relevant. As an important application we also identify a natural equivalence relation that is o ...
On superpositionally measurable semi Carath eodory multifunctions
... a topological space. A multifunction : X ! 2Y is said to be -measurable (resp. weakly -measurable) if the set , (A) = fx 2 X : (x) \ A 6= ;g belongs to for every closed (resp. open) set A Y . It is known (see [2], [3], [13]) that when (X ; ) is a complete measurable space (i.e. there is a ...
... a topological space. A multifunction : X ! 2Y is said to be -measurable (resp. weakly -measurable) if the set , (A) = fx 2 X : (x) \ A 6= ;g belongs to for every closed (resp. open) set A Y . It is known (see [2], [3], [13]) that when (X ; ) is a complete measurable space (i.e. there is a ...
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.