Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Topological Shape Homotopy Groups   In this paper, using the topology on the set of shape morphisms between
arbitrary topological spaces $X$, $Y$, $Sh(X,Y)$, defined by Cuchillo-Ibanez et
al. in 1999, we consider a topology on the shape homotopy groups of arbitrary
topological spaces which make them Hausdorff topological groups. We then
exhibit an example in which $\check{\pi}_k^{top}$ succeeds in distinguishing
the shape type of $X$ and $Y$ while $\check{\pi}_k$ fails, for all $k\in
\Bbb{N}$. Moreover, we present some basic properties of topological shape
homotopy groups, among them commutativity of $\check{\pi}_k^{top}$ with finite
product of compact Hausdorff spaces. Finally, we consider a quotient topology
on the $k$th shape group induced by the $k$th shape loop space and show that it
coincides with the above topology.

12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex