There need not be any such topologies in general You ve noted for example that all constant functions are continuous

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Previous Question: If you pick any topology on Y, then there is a smallest topology on X such that the gi are all continuous (the one generated by all preimages of open sets in Y under the gi). As Cameron points out, there may then be extra continuous functions between X and Y. What isn't immediately clear to me (but I'd be interested to know) is what conditions you need on the set {gi} such that this doesn't happen; this could easily depend on the choice of topology for Y. Alternatively, are there conditions on the gi giving a unique topology on X and Y so they're continuous. Next Question: Using the formulas from above, we can start with x=4: f(4) = 24-4+3 = 11

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There need not be any such topologies in general. You've noted, for example, that all constant functions are continuous, so if your sub-collection of functions does not have all constant functions as elements, then we're out of luck in topologizing X and Y in the desired fashion.: Asked In AIEEE MAN (11 years ago); Unsolved; Is this Puzzle helpful? (0) (0) Submit Your Solution

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Latest AIEEE Aptitude Question SOLUTION: There need not be any such topologies in general. You've noted, for example, that all constant functions are continuous, so if your sub-collection of functions does not have all co

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(#M40022806) AIEEE question FUNCTION Keep an EYE

There need not be any such topologies in general. You've noted, for example, that all constant functions are continuous, so if your sub-collection of functions does not have all constant functions as elements, then we're out of luck in topologizing X and Y in the desired fashion.

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