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... Definition - A subset Y of a topological space X is said to be locally closed if it is the intersection of an open and a closed subset. The following result provides some equivalent definitions: Proposition - The following are equivalent: 1. Y is locally closed in X. 2. Each point in Y has an open n ...
... Definition - A subset Y of a topological space X is said to be locally closed if it is the intersection of an open and a closed subset. The following result provides some equivalent definitions: Proposition - The following are equivalent: 1. Y is locally closed in X. 2. Each point in Y has an open n ...
Linearly Ordered and Generalized Ordered Spaces
... and who proved in essence that a GO-space X is paracompact if and only if whenever G and H are disjoint open sets that cover X and have the property that x < y whenever x ∈ G and y ∈ H, then there are closed discrete subsets C and D of X with the property that C ⊆ G is cofinal in G and D ⊆ H is coin ...
... and who proved in essence that a GO-space X is paracompact if and only if whenever G and H are disjoint open sets that cover X and have the property that x < y whenever x ∈ G and y ∈ H, then there are closed discrete subsets C and D of X with the property that C ⊆ G is cofinal in G and D ⊆ H is coin ...
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... (a) if two edges of the graph intersect then they intersect in a vertex of the graph; (b) each resulting face on the torus is a curvilinear disk (i.e. a “continuous deformation” of some planar polygonal disk). Determine the number of vertices V , edges E and faces F for your graph. Then compute the ...
... (a) if two edges of the graph intersect then they intersect in a vertex of the graph; (b) each resulting face on the torus is a curvilinear disk (i.e. a “continuous deformation” of some planar polygonal disk). Determine the number of vertices V , edges E and faces F for your graph. Then compute the ...