What does topologize in math mean

Topologize in mathematics refers to the process of introducing a topology on a set. A topology is a collection of subsets of the set that satisfy certain axioms, such as the requirement that the union of any two open sets is open, and the intersection of any finite number of open sets is open.

Topologies are used to define notions of continuity, convergence, and connectedness in a set. They also provide a framework for studying the properties of sets and functions.

What is the difference between a topology and a metric?
How are topologies used to define continuity?
What is the Hausdorff topology?
What is the product topology?
How are topologies used in algebraic topology?

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What does topologize in math mean

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