What's the name of this relation between metric spaces?
Frank Wappler
Given two metric spaces, (A, d) and (M, s),
such that there exist
a bijective map f: A <--> M, and
a positive real number k
by which for any two elements x and y of set A holds
s[ f[ x ], f[ y ] ] == k d[ x, y ] ...
... what's the name or technical term of this relation
between these two metric spaces, please?
("metric compatibility"?, "affinity"?, "___-morphism"?, ...).
Or are there perhaps names for some more general relations,
e.g. for (A, d) and (M, s) being pseudometric spaces,
or for f being an injective map?
Thanks a bunch,
Frank
Frank Wappler
Allright, I just figured it out
(putting one's questions before the public is a marvellous way of
concentrating the mind/memory, isn't it? :) --
"scaled isometry"
Thanks again,
Frank
G. A. Edgar
<0fcb7f4d-55a3-47ce...@v30g2000yqm.googlegroups.com>,
Frank Wappler <frwa...@gmail.com> wrote:
> Given two metric spaces, (A, d) and (M, s),
>
> such that there exist
>
> a bijective map f: A <--> M, and
>
> a positive real number k
>
> by which for any two elements x and y of set A holds
>
> s[ f[ x ], f[ y ] ] == k d[ x, y ] ...
This map is a "similitude" and the two spaces are "similar" ...
terminology from elementary geometry. This terminology is used in
fractal geometry, at least, as well as elementary geometry.
>
> ... what's the name or technical term of this relation
> between these two metric spaces, please?
> ("metric compatibility"?, "affinity"?, "___-morphism"?, ...).
>
> Or are there perhaps names for some more general relations,
> e.g. for (A, d) and (M, s) being pseudometric spaces,
> or for f being an injective map?
>
> Thanks a bunch,
>
> Frank
>
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/