کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4658997 1344298 2013 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the topology of free paratopological groups. II
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
On the topology of free paratopological groups. II
چکیده انگلیسی

Let FP(X) be the free paratopological group on a topological space X. For n∈N, denote by FPn(X) the subset of FP(X) consisting of all words of reduced length at most n, and by in the natural mapping from (X⊕X−1⊕{e})n to FPn(X). In this paper a neighbourhood base at the identity e in FP2(X) is found. A number of characterisations are then given of the circumstances under which the natural mapping is a quotient mapping, where X is a T1 space and denotes the set X−1 equipped with the discrete topology. Further characterisations are given in the case where X is a transitive T1 space. Several specific spaces and classes of spaces are also examined. For example, i2 is a quotient mapping for every countable subspace of R, i2 is not a quotient mapping for any uncountable compact subspace of R, and it is undecidable in ZFC whether an uncountable subspace of R exists for which i2 is a quotient mapping.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 160, Issue 1, 1 January 2013, Pages 220-229