answersLogoWhite

0


Best Answer

A pseudometric is a symmetric function: if ρ is a pseudometric on a set X, then ρ(x,y)=ρ(y,x) for all x,y∈X. This means that if τ is the topology on X generated by ρ, and x,y∈X, then

x∈clτ{y} if and only if y∈clτ{x}.

This is not the case with the Sierpiński space, however: in that we have 0∈clτ{1}, not 1∉clτ{0}. Thus, the Sierpiński topology on {0,1} cannot be generated by a pseudometric.

User Avatar

Wiki User

11y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: Why a Sierpinski space is not obtainable from a pseudometric?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

Who made the sierpinski triangle?

Waclaw Sierpinski!!!!!!!!!!!!!!! how can't you find this out!


Who was sierpinski?

Sierpinski refers to Waclaw Sierpinski, a Polish mathematician who made significant contributions to topology, number theory, and set theory. He is particularly known for his work on the Sierpinski triangle and the Sierpinski sieve, which are named after him. He also made important contributions to the theory of functions and the theory of interpolation.


When was Waclaw Sierpinski born?

Waclaw Sierpinski was born on March 14, 1882.


What is Sierpinski triangle?

The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915.


How can you use the sierpinski triangle?

do it


How many triangles are in Sierpinski's triangle?

Well a Sierpinski Triangle is a triangle mad up of 69 small triangles.


Facts about sierpinski tetrahedron?

It has six.


How old is Waclaw Sierpinski?

Waclaw Sierpinski was born on March 14, 1882 and died on October 21, 1969. Waclaw Sierpinski would have been 87 years old at the time of death or 133 years old today.


What are the common fractals?

Sierpinski's Triangle Sierpinski's Carpet The Wheel of Theodorus Mandelbrot Julia Set Koch Snowflake ...Just to name a few(:


Is there a relationship between Sierpinski Gasket and Pascals Triangle?

Yes. If you mark the odd numbers in Pascal's Triangle, it would form Sierpinski's Gasket.


What fractal is represented below?

Sierpinski gasket


What is Waclaw Sierpinski's birthday?

Waclaw Sierpinski was born on March 14, 1882.