The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

We discuss the class of paratopological groups which admits a transversal, T 1 -independent and -complementary group topology. show that Sorgenfrey line does not admit Hausdorff topology, gives negative answer to [5, Problem 10] . give very useful criterion for transversality in term submaximal prove if non-discrete topology G contains central subgroup transversal then so introduce concept PT -...

In this paper, we present a novel approach to machine reading comprehension for the MS-MARCO dataset. Unlike the SQuAD dataset that aims to answer a question with exact text spans in a passage, the MS-MARCO dataset defines the task as answering a question from multiple passages and the words in the answer are not necessary in the passages. We therefore develop an extraction-then-synthesis frame...