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Aalborg Universitet The lattice of d-structures Fajstrup, Lisbeth
... graphs minus a “forbidden area”. In section 4, we take the point of view, that the forbidden area is not removed from the space, but instead, no directed paths (except the constant ones) enter this area. This gives a correspondence between subsets of the space and directed structures: Given a subset ...
... graphs minus a “forbidden area”. In section 4, we take the point of view, that the forbidden area is not removed from the space, but instead, no directed paths (except the constant ones) enter this area. This gives a correspondence between subsets of the space and directed structures: Given a subset ...
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... Corollary 3.4 (See [10]). Let X, Y be topological spaces and let X be Čechcomplete. Let F : Y → X be a compact-valued mapping with a closed graph. Then the set of points of upper semicontinuity of F is a Gδ subset of Y . Corollary 3.5. Let X, Y be topological spaces and let X be locally compact. Let ...
... Corollary 3.4 (See [10]). Let X, Y be topological spaces and let X be Čechcomplete. Let F : Y → X be a compact-valued mapping with a closed graph. Then the set of points of upper semicontinuity of F is a Gδ subset of Y . Corollary 3.5. Let X, Y be topological spaces and let X be locally compact. Let ...
Decompositions of Generalized Continuity in Grill Topological Spaces
... K is a semiG -closed set containing K and hence sG Cl(K) ⊆ IntClG (K) ∪ K. Hence the result. Definition 2.12. Let (X, τ, G) be a grill topological space and K ⊆ X. K is called (1) generated semiG - closed (gsG - closed) in (X, τ, G) if sG Cl(K) ⊆ O whenever K ⊆ O and O is an open set in (X, τ, G); ( ...
... K is a semiG -closed set containing K and hence sG Cl(K) ⊆ IntClG (K) ∪ K. Hence the result. Definition 2.12. Let (X, τ, G) be a grill topological space and K ⊆ X. K is called (1) generated semiG - closed (gsG - closed) in (X, τ, G) if sG Cl(K) ⊆ O whenever K ⊆ O and O is an open set in (X, τ, G); ( ...
3-manifold
![](https://commons.wikimedia.org/wiki/Special:FilePath/3-Manifold_3-Torus.png?width=300)
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.