Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abbott Dimension, Mathematics Inspired by Flatland   In this paper we introduce the Abbott dimension of Hausdorff spaces, an
intuitively defined dimension function inspired by Edwin Abbott's
\emph{Flatland}. We show that on separable metric spaces the Abbott dimension
is bounded above by the large inductive dimension. Consequently we show that
the Abbott dimension of $\mathbb{R}^{n}$ is $n$. We conclude by showing that
hereditarily indecomposable continua all have Abbott dimension $1$, while there
exist such continua of arbitrarily high large inductive, small inductive, and
covering dimension.

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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org