Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spaces of Remote Points   Given a Tychonoff space $X$, let $\varrho(X)$ be the set of remote points of
$X$. We view $\varrho(X)$ as a topological space. In this paper we assume that
$X$ is metrizable and ask for conditions on $Y$ so that $\varrho(X)$ is
homeomorphic to $\varrho(Y)$. This question has been studied before by R. G.
Woods and C. Gates. We give some results of the following type: if $X$ has
topological property $\mathbf{P}$ and $\varrho(X)$ is homeomorphic to
$\varrho(Y)$, then $Y$ also has $\mathbf{P}$. We also characterize the remote
points of the rationals and irrationals up to some restrictions. Further, we
show that $\varrho(X)$ and $\varrho(Y)$ have open dense homeomorphic subspaces
if $X$ and $Y$ are both nowhere locally compact, completely metrizable and
share the same cellular type, a cardinal invariant we define.

37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex