“real: chapter_04” — 2011/5/22 — 23:17 — page2—#2
4-2 Real Analysis
such as limit and continuity. For this also, the system of real numbers
enables us to identify certain concepts that make it possible to define
an abstract metric space and an abstract topological space. Since the
concept of an abstract topological space will lead us to a more general
concept than what is required at present, we shall confine our attention
to those properties of the real number system that can lead us to the
concept of an abstract metric space. It is in this context that most of
the properties of the real line, which can be formulated using the idea
of a distance and an interval are studied here in some detail. However,
we shall first formulate these results with reference ...