Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation by light maps and parametric Lelek maps   The class of metrizable spaces $M$ with the following approximation property
is introduced and investigated: $M\in AP(n,0)$ if for every $\e>0$ and a map
$g\colon\I^n\to M$ there exists a 0-dimensional map $g'\colon\I^n\to M$ which
is $\e$-homotopic to $g$. It is shown that this class has very nice properties.
For example, if $M_i\in AP(n_i,0)$, $i=1,2$, then $M_1\times M_2\in
AP(n_1+n_2,0)$. Moreover, $M\in AP(n,0)$ if and only if each point of $M$ has a
local base of neighborhoods $U$ with $U\in AP(n,0)$. Using the properties of
AP(n,0)-spaces, we generalize some results of Levin and Kato-Matsuhashi
concerning the existence of residual sets of $n$-dimensional Lelek maps.

31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat