Canadian Mathematical Society www.cms.math.ca
Search results

Search: MSC category 54E52 ( Baire category, Baire spaces )

 Expand all        Collapse all Results 1 - 3 of 3

1. CMB Online first

Bernardes, Nilson C.
 Addendum to Limit Sets of Typical Homeomorphisms'' Given an integer $n \geq 3$, a metrizable compact topological $n$-manifold $X$ with boundary, and a finite positive Borel measure $\mu$ on $X$, we prove that for the typical homeomorphism $f : X \to X$, it is true that for $\mu$-almost every point $x$ in $X$ the restriction of $f$ (respectively of $f^{-1}$) to the omega limit set $\omega(f,x)$ (respectively to the alpha limit set $\alpha(f,x)$) is topologically conjugate to the universal odometer. Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit setsCategories:37B20, 54H20, 28C15, 54C35, 54E52

2. CMB 2011 (vol 55 pp. 225)

Bernardes, Nilson C.
 Limit Sets of Typical Homeomorphisms Given an integer $n \geq 3$, a metrizable compact topological $n$-manifold $X$ with boundary, and a finite positive Borel measure $\mu$ on $X$, we prove that for the typical homeomorphism $f \colon X \to X$, it is true that for $\mu$-almost every point $x$ in $X$ the limit set $\omega(f,x)$ is a Cantor set of Hausdorff dimension zero, each point of $\omega(f,x)$ has a dense orbit in $\omega(f,x)$, $f$ is non-sensitive at each point of $\omega(f,x)$, and the function $a \to \omega(f,a)$ is continuous at $x$. Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit setsCategories:37B20, 54H20, 28C15, 54C35, 54E52

3. CMB 2010 (vol 54 pp. 193)

Bennett, Harold; Lutzer, David
 Measurements and $G_\delta$-Subsets of Domains In this paper we study domains, Scott domains, and the existence of measurements. We use a space created by D.~K. Burke to show that there is a Scott domain $P$ for which $\max(P)$ is a $G_\delta$-subset of $P$ and yet no measurement $\mu$ on $P$ has $\ker(\mu) = \max(P)$. We also correct a mistake in the literature asserting that $[0, \omega_1)$ is a space of this type. We show that if $P$ is a Scott domain and $X \subseteq \max(P)$ is a $G_\delta$-subset of $P$, then $X$ has a $G_\delta$-diagonal and is weakly developable. We show that if $X \subseteq \max(P)$ is a $G_\delta$-subset of $P$, where $P$ is a domain but perhaps not a Scott domain, then $X$ is domain-representable, first-countable, and is the union of dense, completely metrizable subspaces. We also show that there is a domain $P$ such that $\max(P)$ is the usual space of countable ordinals and is a $G_\delta$-subset of $P$ in the Scott topology. Finally we show that the kernel of a measurement on a Scott domain can consistently be a normal, separable, non-metrizable Moore space. Keywords:domain-representable, Scott-domain-representable, measurement, Burke's space, developable spaces, weakly developable spaces, $G_\delta$-diagonal, Äech-complete space, Moore space, $\omega_1$, weakly developable space, sharp base, AF-completeCategories:54D35, 54E30, 54E52, 54E99, 06B35, 06F99

© Canadian Mathematical Society, 2013 : http://www.cms.math.ca/