  The kernel of analysis, to me anyway, is the following idea: A point is
arbitrarily close to a set if every neighborhood of the point intersects the
set. Defining ``arbitrarily close'' in this way provides a foundation for
classical results in calculus and real analysis dealing with convergence,
limits, connectedness, limits, continuity, differentiation, integration,
series, and more. This book contains: a thorough introduction to arbitrarily
close; an approach to limits and convergence of sequences using arbitrarily
close as a key first step; the topology of Euclidean spaces stemming from
closed sets; an exploration of the properties of functions like domains,
ranges, and images of sets and sequences; and an introduction to basic aspects
of continuous functions between Euclidean spaces. Even so, ``arbitrarily
close'' reaches deeper than discussed here. The idea is topological in nature
and there is much more to explore.
