Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topologizing Rings of Map Germs: An Order Theoretic Analysis of Germs
  via Nonstandard Methods   Using nonstandard analysis we define a topology on the ring of germs of
functions: $(mathbb R^n,0)\rightarrow(mathbb R,0)$. We prove that this topology
is absolutely convex, Hausdorff, that convergent nets of continuous germs have
continuous germs as limits and that, for continuous germs, ring operations and
compositions are continuous. This topology is not first countable, and, in
fact, we prove that no good first countable topology exists. We give a spectrum
of standard working descriptions for this topology. Finally, we identify this
topological ring as a generalized metric space and examine some consequences.

29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga