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Wikipedia:Reference desk/Archives/Mathematics/2017 April 2

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April 2

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Non-Hausdorff totally disconnected space

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Every totally disconnected space is T1. Is there an example of a space that is totally disconnected but not Hausdorff (T2)? GeoffreyT2000 (talk, contribs) 02:37, 2 April 2017 (UTC)[reply]

According to Steen & Seebach, a modified Fort space is just such a space. --Deacon Vorbis (talk) 04:12, 2 April 2017 (UTC)[reply]

Intuition Behind the Riemann ζ Functional Equation

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Let Then constitutes the functional equation for the Riemann function. The presence of the product is perfectly understandable, inasmuch as the poles of the former coincide with the (trivial) zeroes of the latter; as is also the symmetry with regard to since this value stands midway between ρ's two poles. What poses serious difficulties from an intuitive perspective, however, is the presence of instead of the expected given the fact that always possesses a known closed form in terms of rather than merely for integer values of the argument k. One can, of course, always write but, for all its niceness, the latter appears somewhat contrived, inasmuch as the power of is clearly a contribution of Riemann's rather than Euler's function. — 79.113.203.86 (talk) 14:29, 2 April 2017 (UTC)[reply]