Countable products of spaces of finite sets
We consider the compact spaces sigma_n(I) of subsets of an uncountable set I of cardinality at most n and their countable products. We give a complete classification of their Banach spaces of continuous functions and a partial topological classification.
A characterization of regular averaging operators and its consequences
We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set C to [0, 1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from C to [0, 1] is dense in the supremum norm in the set of all continuous surjections. The nonmetrizable case is also investigated. As a consequence, we obtain a new characterization of Eberlein compact sets.
Familial Cortical Myoclonic Tremor and Epilepsy, an Enigmatic Disorder: From Phenotypes to Pathophysiology and Genetics. A Systematic Review
Background Autosomal dominant familial cortical myoclonic tremor and epilepsy (FCMTE) is characterized by distal tremulous myoclonus, generalized seizures, and signs of cortical reflex myoclonus. FCMTE has been described in over 100 pedigrees worldwide, under several different names and acronyms. Pathological changes have been located in the cerebellum. This systematic review discusses the clinical spectrum, treatment, pathophysiology, and genetic findings. Methods We carried out a PubMed search, using a combination of the following search terms: cortical tremor, myoclonus, epilepsy, benign course, adult onset, familial, and autosomal dominant; this resulted in a total of 77 studies (761 patients; 126 pedigrees) fulfilling the inclusion and exclusion criteria. Results Phenotypic differences across pedigrees exist, possibly related to underlying genetic differences. A “benign” phenotype has been described in several Japanese families and pedigrees linked to 8q (FCMTE1). French patients (5p linkage; FCMTE3) exhibit more severe progression, and in Japanese/Chinese pedigrees (with unknown linkage) anticipation has been suggested. Preferred treatment is with valproate (mind teratogenicity), levetiracetam, and/or clonazepam. Several genes have been identified, which differ in potential pathogenicity. Discussion Based on the core features (above), the syndrome can be considered a distinct clinical entity. Clinical features may also include proximal myoclonus and mild progression with aging. Valproate or levetiracetam, with or without clonazepam, reduces symptoms. FCMTE is a heterogeneous disorder, and likely to include a variety of different conditions with mutations of different genes. Distinct phenotypic traits might reflect different genetic mutations. Genes involved in Purkinje cell outgrowth or those encoding for ion channels or neurotransmitters seem good candidate genes.