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Topics on Continua (Paperback)
Loot Price: R1,767
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Topics on Continua (Paperback)
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Specialized as it might be, continuum theory is one of the most
intriguing areas in mathematics. However, despite being popular
journal fare, few books have thoroughly explored this interesting
aspect of topology. In Topics on Continua, Sergio Macias, one of
the field's leading scholars, presents four of his favorite
continuum topics: inverse limits, Jones's set function T,
homogenous continua, and n-fold hyperspaces, and in doing so,
presents the most complete set of theorems and proofs ever
contained in a single topology volume. Many of the results
presented have previously appeared only in research papers, and
some appear here for the first time. After building the requisite
background and exploring the inverse limits of continua, the
discussions focus on Professor Jones's set function T and continua
for which T is continuous. An introduction to topological groups
and group actions lead to a proof of Effros's Theorem, followed by
a presentation of two decomposition theorems. The author then
offers an in-depth study of n-fold hyperspaces. This includes their
general properties, conditions that allow points of n-fold
symmetric products to be arcwise accessible from their complement,
points that arcwise disconnect the n-fold hyperspaces, the n-fold
hyperspaces of graphs, and theorems relating n-fold hyperspaces and
cones. The concluding chapter presents a series of open questions
on each topic discussed in the book. With more than a decade of
teaching experience, Macias is able to put forth exceptionally
cogent discussions that not only give beginning mathematicians a
strong grounding in continuum theory, but also form an
authoritative, single-source guide through some of topology's most
captivating facets.
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