Example
Consider the function defined by whenever and whenever . Clearly f is continuous everywhere except at x=0, thus quasi-continuous everywhere except at x=0. At x=0, take any open neighborhood U of x. Then there exists an open set such that . Clearly this yields thus f is quasi-continuous.
Read more about this topic: Quasi-continuous Function
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
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