Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bourbaki-complete spaces and Samuel realcompactifiation   This thesis belongs to the area of General Topology and, in particular, to
the field of study of uniform spaces. It is divided in three parts where the
related topics Bourbaki-completeness and Samuel realcompactification are
studied. In the first part of the thesis we study Bourbaki-completeness and
cofinal Bourbaki-completeness (equivalently, uniform strong-paracompactness) of
uniform spaces. In particular, we solve several primary problems related to
products, subspaces, hyperspaces, metric spaces and fine spaces. Moreover, we
show that completeness and cofinal completeness are, respectively, equivalent
to Bourbaki-completeness and cofinal Bourbaki-completeness whenever we consider
uniformities having a base of star-finite covers. In the second part, we embed
the Bourbaki-complete metric spaces (and after, the Bourbaki-complete uniform
spaces) into an universal space. Next, we characterized those metric spaces
which are metrizable by a Bourbaki-complete metric or cofinally
Bourbaki-complete metric. In the third part we characterize the Samuel
realcompact spaces, that is, those uniform spaces which are complete with the
weak uniformity induced by all the real-valued uniformly continuous functions
on the space. It turns out that these are exactly the Bourbaki-complete uniform
spaces having no uniform partition of Ulam-measurable cardinal. Finally, as a
natural step in order to generalize the above result, we study which kind of
metric or uniform spaces satisfy that the Samuel realcompactification and the
Hewitt realcompactification are equivalent.

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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio