Was just wondering can you extend topology to complex spaces? So is the complex space a metric space with a metric that satisfies triangle inequality, symmetry, and positive definiteness?
If any on any space there is a distance function defined, then that space is a metric space. The function $\displaystyle d(z,w) = \left| {z - w} \right| = \sqrt {\left( {{\mathop{\rm Re}\nolimits} (z) - {\mathop{\rm Re}\nolimits} (w)} \right)^2 + \left( {{\mathop{\rm Im}\nolimits} (z) - {\mathop{\rm Im}\nolimits} (w)} \right)^2 } $ is clearly a metric.