We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous. 1. Introduction. All topological spaces under discussion are Tychonoff. A space X is homogeneous if for any two points x, y ∈ X there is a homeomorphism h from X onto itself such that h(x) = y. If bX is a com-pactification of a space X, then bX \ X is c...

Magill's and Rayburn's theorems on the homeomorphism of Stone-ˇ Cech remainders and some of their generalizations to the remainders of arbitrary Hausdorff compactifications of Tychonoff spaces are extended to some class of mappings.

A recent direction within belief revision theory is to develop a theory of belief change for the Horn knowledge representation framework. We consider questions related to the complexity aspects of previous work, leading to questions about Horn envelopes (or Horn LUB’s), introduced earlier in the context of knowledge compilation. A characterization is obtained of the remainders of a Horn belief ...

In this paper‎, ‎we prove a dichotomy theorem for remainders in‎ ‎compactifications of paratopological groups‎: ‎every remainder of a ‎paratopological group $G$ is either Lindel"{o}f and meager or‎ ‎Baire‎. Furthermore, ‎we give a negative answer to a question posed in [D‎. ‎Basile and A‎. ‎Bella‎, ‎About remainders in compactifications of homogeneous spaces‎, ‎Comment‎. ‎Math‎. ‎Univ‎. ‎Caroli...

It is shown that all compactifications of the positive integers N which have metrizable remainders are themselves metrizable. This is done by first proving that each Hausdorff compactification of a noncompact locally compact space is the graph closure in an appropriate space. It is then shown that any two compactifications of N which have homeomorphic metrizable remainders are homeomorphic.

In estimating frequencies given that the signal waveforms are undersampled multiple times, Xia and his collaborators proposed to use a generalized version of Chinese remainder Theorem (CRT), where the moduli are dm1, dm2, · · · , dmk with m1,m2, · · · ,mk being pairwise coprime. If the errors of the corrupted remainders are within d 4 , their schemes are able to construct an approximation of th...