WEDGE SUM Meaning and
Definition
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Wedge sum is a mathematical concept within the field of topology, specifically in the study of spaces and their properties. It refers to the union of two spaces that are "glued" together at a single point. The resulting space obtained from this operation is known as the wedge sum.
To understand the idea of wedge sum better, consider taking two distinct spaces, typically topological spaces, and select one point from each space to be identified and merged. The resulting space forms the wedge sum, where the two spaces are joined together at these identified points.
The wedge sum construction is commonly used to build new spaces by combining simpler ones. It allows topologists to investigate and analyze properties of spaces by breaking them down into their constituent parts and examining their behavior individually or collectively.
Mathematically speaking, the wedge sum operation is commutative, meaning that the order in which the spaces are combined does not affect the resulting space. Furthermore, the wedge sum preserves certain topological properties, such as homotopy type, homology groups, and fundamental group.
The term "wedge sum" arises from its geometric visualization. It can be thought of as an operation similar to sticking two objects together, such as two slices of pizza, at a common point, creating a union or combination. This visual representation aids in understanding the concept and its application in topology.
Etymology of WEDGE SUM
The term "wedge sum" does not have a specific etymology on its own. However, to understand its meaning, it is helpful to examine the origins of the individual words involved.
- "Wedge" originates from the Old English word "wecg", meaning a mass with a pointed shape. Over time, "wedge" has come to represent a triangular or tapering piece of material, often used to secure or separate objects.
- "Sum" stems from the Latin word "summa", which means a total or the highest point. It has evolved to signify the result of adding numbers together or the whole produced by combining parts.
When these terms are used together, "wedge sum" typically refers to a mathematical operation that combines two topological spaces by gluing their boundaries with a wedge point.
