Pozyskać Królestwo Polskie. Z dokumentacji Sekretariatu Generalnego Naczelnego Komitetu Narodowego z 1914 r. i pierwszej połowy 1915 r.

R/Z Index Theory

We define topological and analytic indices in R/Z K-theory and show that they are equal.

An Irrational Construction of R from Z

This paper reports on a construction of the real numbers in the ProofPower implementation of the HOL logic. Since the original construction was implemented, some major improvements to the ideas have been discovered. The improvements involve some entertaining mathematics: it turns out that the Dedekind cuts provide many routes one can travel to get from the ring of integers, Z, to the field of r...

DISTORTION ELEMENTS IN Diff ∞ (R/Z)

We consider the group of smooth diffeomorphisms of the circle. We show that any recurrent f (in the sense that {f}n∈Z is not discrete) is in fact a distortion element (in the sense that its iterates can be written as short compositions involving finitely many smooth diffeomorphisms). Thus rotations are distortion elements.

Florence R. Sabin, 1915

Sums of Strongly z-Ideals and Prime Ideals in ${mathcal{R}} L$

It is well-known that the sum of two $z$-ideals in $C(X)$ is either $C(X)$ or a $z$-ideal. The main aim of this paper is to study the sum of strongly $z$-ideals in ${mathcal{R}} L$, the ring of real-valued continuous functions on a frame $L$. For every ideal $I$ in ${mathcal{R}} L$, we introduce the biggest strongly $z$-ideal included in $I$ and the smallest strongly $z$-ideal containing ...