A Study of Linear Space – Geometryof Banach Spaces

In mathematics, space is an unbounded continuum (unbroken set of points) in which exactly three numerical coordinates are necessary to uniquely define the location of any particular point. It is sometimes called 3-D space because it contains three distance dimensions. If a continuum requires fewer or more than three coordinates (dimensions) to uniquely define the location of a point, that continuum is sometimes called n-space or n-dimensional space, where n is the number of dimensions. Thus, for example, a line constitutes 1-space and a plane constitutes 2-space. When time is considered as a dimension along with the usual three in conventional space, the result is sometimes called 4-space, 4-dimensional space, time-space, or space-time. Spatial understandings are necessary for interpreting, understanding, and appreciating our inherently geometric world. Insights and intuitions about two- and three-dimensional shapes and their characteristics, the interrelationships of shapes, and the effects of changes to shapes are important aspects of spatial sense. Children who develop a strong sense of spatial relationships and who master the concepts and language of geometry are better prepared to learn number and measurement idea. Arithmetic is an important corner of mathematics, but too often we neglect the rest of the field. Geometry suffers because we have the mistaken impression that it doesn't become real, serious mathematics until it gets abstract and we deal with proof. But geometry is important, even in its less formal form.