Concerning continua in a separable space which do not cross
نویسندگان
چکیده
منابع مشابه
Concerning Continua in a Separable Space Which Do Not Cross*
In working with collections of continua it is sometimes useful to know something of the character of the point set consisting of all the points common to two or more members of the collection. Also it is of advantage to know conditions under which we may subtract a countable number of continua from the collection and have left a collection of mutually exclusive continua. The theorem which we sh...
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We construct a space havfng the properties in the title, and with the same technique, a countably compact T2 topological group which is not absolutely countably compact.
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In 1968 Wilansky asked whether a separable normal topological group must be Lindelof. In [7] this question was answered in the negative, assuming CH, by constructing a hereditarily separable, normal group which is not Lindeliif. We give an example of a separable normal group which contains a closed subspace homeomorphic to an uncountable regular cardinal, in ZFC only. Of course we have to sacri...
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In this paper propositions will be established concerning the collection of all the cut points of a given planef continuum. It will be shown that there does not exist an uncountable collection of mutually exclusive subcontinua of a given continuum M each of which contains at least one cut point of M. With the aid of this fundamental theorem it is shown, among other things, that the set of all t...
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Introduction. One might judge from the title that I am going to discuss continua. For is not a continuum either aposyndetic or nonaposyndetic? What I intend to do is to consider continua from a certain point of view, and from this point of view continua may be classified in a rough sort of way. This system of classification (and the basic concept upon which it rests) is only in its infancy. Her...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1939
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1939-06909-7