Mathematics Asked by user856180 on December 28, 2020

Let (M,d) be a metric space, and M1, M2 be two subspace of M.

Edit: I forgot to mension that both M1 and M2 are dense.

Suppose we have

$f: M rightarrow M$

and we know f is an isometric mapping from M1 to M1, i.e.,

$$

d(f(a),f(b))=d(a,b)

$$

for any $a,b in M1$.

Suppose we also have

$$

d(f(a),f(b))=d(a,b)

$$

for any $a in M1$ and $b in M2$.

The question is : can we say that f is an isometric mapping of $M1cup M2$?

In other words, is it possible to show that

$$

d(f(a),f(b))=d(a,b)

$$

for any $a,b in M1cup M2$.

I think it is true in Euclidean space, but I have no idea how to do it in a general metric space.

Any suggestion would be greatly appreciated.

$M_1={a}$, $M_2={b,c}$, $f(a)=a, f(b)=f(c)=b$, $d(x,y)=1$ if $xneq y.$

Answered by Tsemo Aristide on December 28, 2020

Get help from others!

Recent Questions

- How can I transform graph image into a tikzpicture LaTeX code?
- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?

Recent Answers

- Lex on Does Google Analytics track 404 page responses as valid page views?
- haakon.io on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP