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Base (topology) – Collection of open sets used to define a topology; Filter (set theory) – Family of sets representing "large" sets; Filters in topology – Use of filters to describe and characterize all basic topological notions and results. Locally convex topological vector space – A vector space with a topology defined by convex open sets
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In topology, a second-countable space, also called a completely separable space, is a topological space whose topology has a countable base.More explicitly, a topological space is second-countable if there exists some countable collection = {} = of open subsets of such that any open subset of can be written as a union of elements of some subfamily of .
For example, the Euclidean topology on the plane admits as a base the set of all open rectangles with horizontal and vertical sides, and a nonempty intersection of two such basic open sets is also a basic open set. But another base for the same topology is the collection of all open disks; and here the full (B2) condition is necessary.
The compact-open topology on the space of continuous functions from to has for a subbase the set of functions (,) = {: ()} where is compact and is an open subset of . Suppose that ( X , τ ) {\displaystyle (X,\tau )} is a Hausdorff topological space with X {\displaystyle X} containing two or more elements (for example, X = R {\displaystyle X ...
A scrolled base is similar to the fully enclosed base but it has areas of the base material removed, often with a decorative pattern, leaving feet on which the cabinet stands. Bracket feet are separate feet, usually attached in each corner and occasionally for larger pieces in the middle of the cabinet.
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