DOI: 10.1017/s0004972726101737 ISSN: 0004-9727

A NOTE ON TOPOLOGICAL ASPECTS OF TRANSCENDENTAL SELF-POWERS

SIDNEY A. MORRIS, MARCELO O. RIBEIRO
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Abstract

We study the self-power map

x ↦ x x $x \mapsto x^x$ x right arrow from bar x Superscript x
on
( 0 , ∞ ) $(0,\infty )$ left parenthesis 0 comma infinity right parenthesis
from a topological perspective. In particular, we show that the set of
x > 0 $x> 0$ x greater than 0
, for which
x x $x^x$ x Superscript x
is a Liouville number, is topologically large, but metrically small.

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