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Concerning nearly metrizable spaces - RiuNet
... It is easy to see that every embedding is a pseudo-embedding; but the converse is false as is shown in the following example. Example 2.2. Let R be the set of all real numbers; and, τf and τc be respectively the co-finite topology and the co-countable topology on R. Since τf ⊆ τc , the identity map ...
... It is easy to see that every embedding is a pseudo-embedding; but the converse is false as is shown in the following example. Example 2.2. Let R be the set of all real numbers; and, τf and τc be respectively the co-finite topology and the co-countable topology on R. Since τf ⊆ τc , the identity map ...
256B Algebraic Geometry
... we define the stalk Fx as the colimit of the F (U ) over all open sets U containing x. We then define F + (U ) to be the set of all assignments σx , where x ∈ U and σx ∈ Fx , such that for all x ∈ U there is x ∈ V ⊆ U and σ ∈ F (V ) such that σ restricts to σy for all y ∈ V . Generally speaking, the ...
... we define the stalk Fx as the colimit of the F (U ) over all open sets U containing x. We then define F + (U ) to be the set of all assignments σx , where x ∈ U and σx ∈ Fx , such that for all x ∈ U there is x ∈ V ⊆ U and σ ∈ F (V ) such that σ restricts to σy for all y ∈ V . Generally speaking, the ...
