Applications of some strong set-theoretic axioms to locally compact
... Proof. Let H be an open Lindelöf [resp. ω1 -compact] subset of a space X as described. It is enough to show that H has a boundary with countable spread, since MA(ω1 ) implies every locally compact space of countable spread is hereditarily separable and hereditarily Lindelöf by Szentmiklóssy’s The ...
... Proof. Let H be an open Lindelöf [resp. ω1 -compact] subset of a space X as described. It is enough to show that H has a boundary with countable spread, since MA(ω1 ) implies every locally compact space of countable spread is hereditarily separable and hereditarily Lindelöf by Szentmiklóssy’s The ...
Compact operators on Banach spaces
... and F xi = yn for i ≥ n. With T 0 = T + F again, in this case T 0 − λ is surjective, so is injective, and m = n. ...
... and F xi = yn for i ≥ n. With T 0 = T + F again, in this case T 0 − λ is surjective, so is injective, and m = n. ...
computational topology
... A Path is a continuous function γ : [0, 1] → X . Connecting γ(0) to γ(1) in X . Self intersections are allowed (there can be s, t ∈ [0, 1] such that γ(s) = γ(t)). No self intersections ⇒ the function is injective and the path is ...
... A Path is a continuous function γ : [0, 1] → X . Connecting γ(0) to γ(1) in X . Self intersections are allowed (there can be s, t ∈ [0, 1] such that γ(s) = γ(t)). No self intersections ⇒ the function is injective and the path is ...
EBERLEIN–ŠMULYAN THEOREM FOR ABELIAN TOPOLOGICAL
... fundamental tool, and the optimal situation is when it can be used in its sequential version. Unfortunately this is not always the case, and there is a strong need to look for classes of topological spaces where compactness is equivalent to sequential or countable compactness. It was known from the ...
... fundamental tool, and the optimal situation is when it can be used in its sequential version. Unfortunately this is not always the case, and there is a strong need to look for classes of topological spaces where compactness is equivalent to sequential or countable compactness. It was known from the ...
Let (X, τ) be a topological space, a base B is a
... Let (X, τ ) be a topological space, a base B is a subset of τ such that each element of τ could be written as an union of element from B, every base i) covers X and ii) has the property that the intersection of any two base sets contains another base set (and conversely every subset of 2X which sati ...
... Let (X, τ ) be a topological space, a base B is a subset of τ such that each element of τ could be written as an union of element from B, every base i) covers X and ii) has the property that the intersection of any two base sets contains another base set (and conversely every subset of 2X which sati ...
Topology Final (Math 222) Doğan Bilge 2005 1. Let X be a
... Then A and B are closed in X. Hence there are disjoint open subsets U and V of X containing A and B respectively. Then U ∩ Y and V ∩ Y are disjoint open subsets of Y containing A and B respectively. 5. Let X be a totally ordered set. Let ℑ be the collection of all sets of the following types: (1) Op ...
... Then A and B are closed in X. Hence there are disjoint open subsets U and V of X containing A and B respectively. Then U ∩ Y and V ∩ Y are disjoint open subsets of Y containing A and B respectively. 5. Let X be a totally ordered set. Let ℑ be the collection of all sets of the following types: (1) Op ...
HYPERBOLIZATION OF POLYHEDRA
... announced some related results concerning the ideal boundary of these reflection group examples; in particular, they have pointed out that the ideal boundary need not be a sphere (or even an ANR). It has been known since 1975 that polyhedral homology manifolds which are not PL manifolds can unexpect ...
... announced some related results concerning the ideal boundary of these reflection group examples; in particular, they have pointed out that the ideal boundary need not be a sphere (or even an ANR). It has been known since 1975 that polyhedral homology manifolds which are not PL manifolds can unexpect ...