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real analysis studies the behavior of real numbers, sequences and
series of real numbers, and real functions.[1]
Some particular properties of real-valued sequences and functions that real analysis studies
include convergence, limits, continuity, smoothness, differentiability and integrability.

topology is concerned with the properties of a geometric object
that are preserved under continuous deformations,
such as stretching, twisting, crumpling and bending, but not tearing or gluing.

Many of the theorems of real analysis are consequences of the topological properties of the real number line.
The order properties of the real numbers described above are closely related to these topological properties.

Informally, a topology tells how elements of a set relate spatially to each other.
The same set can have different topologies.
For instance, the real line, the complex plane, and the Cantor set
can be thought of as the same set with different topologies.

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