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Math Help - Topology in Complex Space?

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    Topology in Complex Space?

    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?
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    Quote Originally Posted by shilz222 View Post
    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?
    Roughly complex spaces can be thought of as real spaces with twice the number of dimensions.

    RonL
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    Quote Originally Posted by shilz222 View Post
    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?
    The topology in \mathbb{C} can be tought as \mathbb{R}^2 (as CaptainBlank says) with the metric d((x_1,x_2),(y_1,y_2)) = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}.
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    If any on any space there is a distance function defined, then that space is a metric space. The function 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.
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