Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak similarities of metric and semimetric spaces   Let (X,dX) and (Y,dY) be semimetric spaces with distance sets D(X) and,
respectively, D(Y). A mapping F : X \to Y is a weak similarity if it is
surjective and there exists a strictly increasing f : D(Y) \to D(X) such that
dX = f \circ dY \circ F. It is shown that the weak similarities between
geodesic spaces are usual similarities and every weak similarity F : X \to Y is
an isometry if X and Y are ultrametric and compact with D(X) = D(Y). Some
conditions under which the weak similarities are homeomorphisms or uniform
equivalences are also found.

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The categories of this paper are: alg-geom
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat