Topology

Characterization of monovalued reloids with atomic domains ★★

Author(s): Porton

Conjecture   Every monovalued reloid with atomic domain is either
  1. an injective reloid;
  2. a restriction of a constant function

(or both).

Keywords: injective reloid; monovalued reloid

Posted by porton
updated October 26th, 2010
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Topology

Composition of reloids expressed through atomic reloids ★★

Author(s): Porton

Conjecture   If $ f $ and $ g $ are composable reloids, then $$g \circ f = \bigcup \{G \circ F | F \in \mathrm{atoms}\, f, G \in \mathrm{atoms}\, g \}.$$

Keywords: atomic reloids

Posted by porton
updated October 26th, 2010
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Number Theory » Analytic N.T.

Lindelöf hypothesis ★★

Author(s): Lindelöf

Conjecture   For any $ \epsilon>0 $ $$\zeta\left(\frac12 + it\right) \mbox{ is }\mathcal{O}(t^\epsilon).$$

Since $ \epsilon $ can be replaced by a smaller value, we can also write the conjecture as, for any positive $ \epsilon $, $$\zeta\left(\frac12 + it\right) \mbox{ is }o(t^\varepsilon).$$

Keywords: Riemann Hypothesis; zeta

Posted by porton
updated September 20th, 2010
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Topology

Outer reloid of direct product of filters ★★

Author(s): Porton

Question   $ ( \mathsf{\tmop{RLD}})_{\tmop{out}} ( \mathcal{A} \times^{\mathsf{\tmop{FCD}}} \mathcal{B}) = \mathcal{A} \times^{\mathsf{\tmop{RLD}}} \mathcal{B} $ for every f.o. $ \mathcal{A} $, $ \mathcal{B} $?

Keywords: direct product of filters; outer reloid

Posted by porton
updated September 4th, 2010
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