Top

A top is a toy designed to be spun rapidly on the ground, the motion of which causes it to remain precisely balanced on its tip because of inertia. Such toys have existed since antiquity. Traditionally tops were constructed of wood, sometimes with an iron tip, and would be set in motion by aid of a string or rope coiled around its axis which, when pulled quickly, caused a rapid unwinding that would set the top in motion. Today they are often built of plastic, and modern materials and manufacturing processes allow tops to be constructed with such precise balance that they can be set in motion by a simple twist of the fingers and twirl of the wrist without need for string or rope.

Characteristics

The motion of a top is produced in the most simple forms by twirling the stem using the fingers. More sophisticated tops are spun by holding the axis firmly while pulling a string or twisting a stick or pushing an auger. In the kinds with an auger, an internal weight rotates, producing an overall circular motion. Some tops can be thrown, while firmly grasping a string that had been tightly wound around the stem, and the centrifugal force generated by the unwinding motion of the string will set them spinning upon touching ground.

Top (clothing)

A top is clothing that covers at least the chest, but which usually covers most of the upper human body between the neck and the waistline. The bottom of tops can be as short as mid-torso, or as long as mid-thigh. Men's tops are generally paired with pants, and women's with pants or skirts. Common types of tops are t-shirts, blouses and shirts.

Design

The neckline is the highest line of the top, and may be as high as a head-covering hood, or as low as the waistline or bottom hem of the top. A top may be worn loose or tight around the bust or waist, and may have sleeves or shoulder straps, spaghetti straps (noodle straps), or may be strapless. The back may be covered or bare. Tops may have straps around the waist or neck, or over the shoulders.

Types

Neck styles

See also

References

External links

Category of topological spaces

In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps or some other variant; for example, objects are often assumed to be compactly generated. This is a category because the composition of two continuous maps is again continuous. The study of Top and of properties of topological spaces using the techniques of category theory is known as categorical topology.

N.B. Some authors use the name Top for the category with topological manifolds as objects and continuous maps as morphisms.

As a concrete category

Like many categories, the category Top is a concrete category (also known as a construct), meaning its objects are sets with additional structure (i.e. topologies) and its morphisms are functions preserving this structure. There is a natural forgetful functor

to the category of sets which assigns to each topological space the underlying set and to each continuous map the underlying function.

Tree (data structure)

In computer science, a tree is a widely used abstract data type (ADT)--or data structure implementing this ADT--that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes.

A tree data structure can be defined recursively (locally) as a collection of nodes (starting at a root node), where each node is a data structure consisting of a value, together with a list of references to nodes (the "children"), with the constraints that no reference is duplicated, and none points to the root.

Alternatively, a tree can be defined abstractly as a whole (globally) as an ordered tree, with a value assigned to each node. Both these perspectives are useful: while a tree can be analyzed mathematically as a whole, when actually represented as a data structure it is usually represented and worked with separately by node (rather than as a list of nodes and an adjacency list of edges between nodes, as one may represent a digraph, for instance). For example, looking at a tree as a whole, one can talk about "the parent node" of a given node, but in general as a data structure a given node only contains the list of its children, but does not contain a reference to its parent (if any).

Tree (Gaelic Storm album)

Tree is a 2001 album by Gaelic Storm.

Track listing

Beggarman, Black is the Colour, New York Girl, An Poc Ar Buile, and Go Home Girl are traditionals. Beggarman, which is played fast, is a standard in their live set list and features a didgeridoo very prominently. Black is the Colour, sung by guitarist Steve Twigger, is very slow and mournful, reminiscent of the original composition from the previous album She Was the Prize. An Poc Ar Buile is the band's first venture in the Irish language. The song is normally slowly sung, but Gaelic Storm puts a twist into it by singing it fast, complete with hoots and hollers. Go Home, Girl is a faster tune about a girl who falls in love with a gypsy, only to have her advances turned down for an ironic reason.

2–3–4 tree

In computer science, a 2–3–4 tree (also called a 2–4 tree) is a self-balancing data structure that is commonly used to implement dictionaries. The numbers mean a tree where every node with children (internal node) has either two, three, or four child nodes:

2-node

2-node

3-node

3-node

4-node

4-node

2–3–4 trees are B-trees of order 4; like B-trees in general, they can search, insert and delete in O(log n) time. One property of a 2–3–4 tree is that all external nodes are at the same depth.

2–3–4 trees are an isometry of red–black trees, meaning that they are equivalent data structures. In other words, for every 2–3–4 tree, there exists at least one red–black tree with data elements in the same order. Moreover, insertion and deletion operations on 2–3–4 trees that cause node expansions, splits and merges are equivalent to the color-flipping and rotations in red–black trees. Introductions to red–black trees usually introduce 2–3–4 trees first, because they are conceptually simpler. 2–3–4 trees, however, can be difficult to implement in most programming languages because of the large number of special cases involved in operations on the tree. Red–black trees are simpler to implement, so tend to be used instead.