Meaning of the word topological

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when we say "a topological action", do we only mean that the action is metric free? or is there some other meaning for this expression? What does the word topological mean exactly? Thanks!
 
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It usually means that the given transformation is a continuous one so that the object before the transformation and the object after the transformation are 'topologically' equivalent. If you familiar with the concept of topological equivalent, it may be helpful.
 
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