0.1. This paper presents an investigation of the following problem. Exhibit a class X of topological spaces which contains all peano spaces and which has the following properties: (1) a cyclic element theory exists in each space of the class, (2) the abstract set consisting of all cyclic element of any space X of the class can be topologized so as to be a member of the class X, and (3) the hype...

It is proved that a continuum is a tree if and only if each two connected subsets meet in a connected set. In this note a continuum is a compact connected Hausdorff space. A tree is a continuum in which distinct points are never conjugate [6], i.e., any two distinct points are separated by the deletion of some third point. A dendrite is a metrizable tree. The literature is replete with characte...

1: Although Bayes’s theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes’s theorem sometimes generates sensible procedures from improper priors. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory prompting some authors to insist that all priors be proper. Our model begins wi...

This paper documents the number-related properties of Dëne Sųłiné (Athapaskan). Dëne Sųłiné has neither number inflection nor numeral classifiers. Nouns are bare, occur as such in argument positions, and combine directly with numerals. With these traits, Dëne Sųłiné represents a type of language that is little considered in formal typologies of number and countability. The paper critiques one i...

The issue of whether nouns in Mandarin Chinese can be distinguished into count and mass nouns has been debated in recent literature. Unlike English, Mandarin Chinese is a language where nouns are not obviously count nouns or mass nouns. In fact, syntactically nouns in Mandarin are similar to mass nouns in English, as they cannot combine directly with numerals, but must combine with classifiers;...

Let us call a set A C o' of functions from X into X a-bounded if there is a countable sequence of functions (a.: n E o} C w' such that every member of A is pointwise dominated by an element of that sequence. We study in this paper definability questions concerning this notion of smallness for subsets of o'. We show that most of the usual definability results about the structure of countable sub...

At the turn of the 21st century Agata Smoktunowicz constructed the first example of a nil algebra over a countable field such that the polynomial ring over the algebra is not nil. This answered an old question of Amitsur. We present a simplification of the example. Introduction This monograph began as the author’s earnest attempt to understand the beautiful example constructed in [1], and was o...

and Applied Analysis 3 The quasi-uniform space X,U will always be considered to be a topological space with the topology obtained by using as the family of all neighborhoods of a point x0 ∈ X all sets of the formU x0 {x ∈ X : x0, x ∈ U}, whereU runs overU. Such a topology is called topology of the quasi-uniformity. Note that each topology onX is induced by a quasi-uniformity see 8, 9 , the most...

doi:10.2471/BLT.08.055954 While ethics in health care dates back at least to the times of Hippocrates, Sun Si Miao,1 and Ibn Sina (Avicenna),2 the field of “bioethics” did not emerge until after World War Two. The birth of bioethics was stimulated by a confluence of factors. First, the Nazis’ medical experiments on concentration camp prisoners heightened concerns about the vulnerability of huma...