Continuity of a homomorphism on commutative subalgebras is not sufficient for continuity

A non-commutative Lévy-Cramér continuity theorem

The classical Lévy-Cramér continuity theorem asserts that the convergence of the characteristic functions implies the weak convergence of the corresponding probability measures. We extend this result to the setting of non-commutative probability theory and discuss some applications. ∗CNRS, Université de Provence, Université de la Méditerranée, Université du Sud Toulon-Var. 2 V. Jakšić, Y. Pautr...

Continuity , not change

a study of the rule ‘unforgivable in continuity (survival, sustainability) is not unforgivable in the beginning’

in islamic jurisprudence we face phrases such as ‘unforgivable in continuity (survival, sustainability) is not unforgivable in the beginning’ whose context suggest that this is considered by scholars as a known and accepted rule. but, after examining the traces of the phrase in the books of jurisprudence and rules of islamic jurisprudence, there seems to be no consensus as regards the authentic...

Density Continuity Versus Continuity

Real-valued functions of a real variable which are continuous with respect to the density topology on both the domain and the range are called density continuous. A typical continuous function is nowhere density continuous. The same is true of a typical homeomorphism of the real line. A subset of the real line is the set of points of discontinuity of a density continuous function if and only if...

Continuity is Geometricity

This paper is largely a review of known results about various aspects of geometric logic. Following Grothendieck’s view of toposes as generalized spaces, one can take geometric morphisms as generalized continuous maps. The constructivist constraints of geometric logic guarantee the continuity of maps constructed, and can do so from two different points of view: for maps as point transformers an...