On continuous extensions of grafting maps

study of hash functions based on chaotic maps

توابع درهم نقش بسیار مهم در سیستم های رمزنگاری و پروتکل های امنیتی دارند. در سیستم های رمزنگاری برای دستیابی به احراز درستی و اصالت داده دو روش مورد استفاده قرار می گیرند که عبارتند از توابع رمزنگاری کلیددار و توابع درهم ساز. توابع درهم ساز، توابعی هستند که هر متن با طول دلخواه را به دنباله ای با طول ثابت تبدیل می کنند. از جمله پرکاربردترین و معروف ترین توابع درهم می توان توابع درهم ساز md4, md...

On open extensions of maps

N ov 2 00 4 On continuous extension of grafting maps

The definition of the grafting operation for quasifuchsian groups is extended by Bromberg [Br] to all b-groups. Although the grafting maps are not necessarily continuous at boundary groups, in this paper, we show that the grafting maps take every " standard " convergent sequence to a conver-gent sequence. As a consequence of this result, we extend Goldman's grafting theorem for quasifuchsian gr...

On the pointfree counterpart of the local definition of classical continuous maps

The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...

Continuous Cofinal Maps on Ultrafilters

An ultrafilter U on a countable base set B has continuous Tukey reductions if whenever an ultrafilter V is Tukey reducible to U , then every monotone cofinal map f : U → V is continuous with respect to the Cantor topology, when restricted to some cofinal subset of U . We show that the slightly stronger property of having basic Tukey reductions is inherited under Tukey reducibility. It follows t...