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The fourth and final volume in this comprehensive set presents the
maximum principle as a wide ranging solution to nonclassical,
variational problems. This one mathematical method can be applied
in a variety of situations, including linear equations with
variable coefficients, optimal processes with delay, and the jump
condition. As with the three preceding volumes, all the material
contained with the 42 sections of this volume is made easily
accessible by way of numerous examples, both concrete and abstract
in nature.
General topology is the domain ofmathematics devoted to the
investigation of the concepts of continuity and passage to a limit
at their natural level of generality. The most basic concepts of
general topology, that of a topological space and a continuous map,
were introduced by Hausdorffin 1914.
Oneofthecentralproblemsoftopologyisthedeterminationandinvestigation
of topological invariants; that is, properties ofspaces which are
preserved under homeomorphisms. Topological invariants need not be
numbers. Connectedness, compactness, andmetrizability, forexample,
arenon-numericaltopologicalinvariants.Dimen sional invariants, on
the otherhand, areexamplesofnumericalinvariants which take
integervalues on specific topological spaces. Part II ofthis book
is devoted to them. Topological invariants which take values in the
cardinal numbers play an especially important role, providing the
raw material for many useful coin" putations. Weight, density,
character, and Suslin number are invariants ofthis type. Certain
classes of topological spaces are defined in terms of topological
in variants. Particularly important examples include the metrizable
spaces, spaces with a countable base, compact spaces, Tikhonov
spaces, Polish spaces, Cech complete spaces and the symmetrizable
spaces."
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