Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Points of continuity of quasiconvex functions on topological vector
  spaces   We give necessary and sufficient conditions for a real-valued quasiconvex
function f on a Baire topological vector space X (in particular, Banach or
Frechet space) to be continuous at the points of a residual subset of X. These
conditions involve only simple topological properties of the lower level sets
of f. A main ingredient consists in taking advantage of a remarkable property
of quasiconvex functions relative to a topological variant of essential extrema
on the open subsets of X. One application is that if f is quasiconvex and
continuous at the points of a residual subset of X, then with a single possible
exception, f^{-1}(a) is nowhere dense or has nonempty interior, as is the case
for everywhere continuous functions. As a barely off-key complement, we also
prove that every usc quasiconvex function is quasicontinuous in the (classical)
sense of Kempisty since this interesting property does not seem to have been
noticed before.

30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an