The dimension formula is that the dimension of sum space is equal to the sum of space dimensions, and the dimension of intersection space decreases. Dim(V+U)= dimV+ moody -dim(V∩U). For example, in three-dimensional space, the sum space of two-dimensional space where xOy plane is located and two-dimensional space where yOz plane is located is three-dimensional space, and the intersection space between them is one-dimensional Y axis.

If the intersection space is zero space {0} and its dimension is zero, the sum space can be decomposed into direct sum: dim(V⊕U)=dimV+dimU For example, the direct sum of one-dimensional space of X axis and two-dimensional space of yOz plane is three-dimensional space.

Theorem assertion:

Theorem asserts that for any natural number n, there are H. L. Brouwer (Brouwer, L.E.J) whose IndR "= IndR" = N. DimR "= N is 19 1 1 year.

Ind R" = n proved by Brouwer (Brouwer, L.E.J) in 19 13. Ind R" = n was proved by Menger (K K.) in 1924 and Uryson (YPMCON, II.C) in 6544.

One dimension has only length.

The two-dimensional plane world is only wide and long.

A three-dimensional world with length, width and height. The three-dimensional world we see with naked eyes is a space where the position of a point is determined by three coordinates. The real space of objective existence is a three-dimensional space with three dimensions: length, width and height. The concept of multidimensional space introduced in mathematics, physics and other disciplines is a scientific abstraction based on three-dimensional space.

The concept of four-dimensional space-time Most of the four-dimensional space mentioned in daily life refers to the concept of four-dimensional space-time mentioned by Albert Einstein in General Relativity and Special Relativity.

Our universe is made up of time and space. The relationship between time and space is to add a time axis to the three axes of length, width and height of ordinary three-dimensional space, and this time axis is an imaginary axis. According to Albert Einstein's theory of relativity, the three-dimensional space we face in life and time constitutes the so-called four-dimensional space.