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Pyometra in a dog. The most obvious symptom of open pyometra is a discharge of pus from the vulva in a female that has recently been in heat. However, symptoms of closed pyometra are less obvious. Symptoms of both types include vomiting, loss of appetite, depression, and increased drinking and urinating. [1]
In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. [1] [2] [3] That is, a function : is open if for any open set in , the image is open in . Likewise, a closed map is a function that maps closed sets to closed sets.
In object-oriented programming, the open–closed principle (OCP) states " software entities (classes, modules, functions, etc.) should be open for extension, but closed for modification "; [1] that is, such an entity can allow its behaviour to be extended without modifying its source code. The name open–closed principle has been used in two ...
Closed and exact differential forms. In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα = 0), and an exact form is a differential form, α, that is the exterior derivative of another differential form β. Thus, an exact form is in the image of d ...
A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, in the Friedmann–Lemaître–Robertson–Walker (FLRW) model, the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.
Ball (mathematics) In Euclidean space, a ball is the volume bounded by a sphere. In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. [1] It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them). These concepts are defined not only in three ...
Example: the blue circle represents the set of points (x, y) satisfying x 2 + y 2 = r 2.The red disk represents the set of points (x, y) satisfying x 2 + y 2 < r 2.The red set is an open set, the blue set is its boundary set, and the union of the red and blue sets is a closed set.
Bracket (mathematics) In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets , are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in ...