A Hilbert Cube L-S Category

Factoring the Hilbert Cube

In 1964, R. D. Anderson announced [ l ] that the product of a countably infinite collection of dendra is a Hilbert cube (a dendron being a nondegenerate, uniquely arcwise connected, Peano continuum). He and R. H. Bing conjectured in [4] that a countably infinite product of compact contractible complexes is a Hilbert cube. The purpose of this note is to announce the following theorems which affi...

A radical extension of the category of $S$-sets

Let S-Set be the category of $S$-sets, sets together with the actions of a semigroup $S$ on them. And, let S-Pos be the category of $S$-posets, posets together with the actions compatible with the orders on them. In this paper we show that the category S-Pos is a radical extension of S-Set; that is there is a radical on the category S-Pos, the order desolator radical, whose torsion-free class i...

Fake Boundary Sets in the Hilbert Cube

For each positive integer n, a o-Z-set B„ in the Hilbert cube 7°° is constructed whose complement s„ = Ix — B„ is not homeomorphic to the pseudointerior j of the Hilbert cube though sn and B„ satisfy: (i) every compact subset of s„ is a Z-set in s„; (ii) s„ X s„ is homeomorphic to s; (iii) Bn admits small maps 7°° -» B„; (iv) s„ satisfies the discrete «-cells property; and (v) Bn is locally (n ...

2 ' Is Homeomorphic to the Hilbert Cube

On a New Reverse Hilbert\'s Type Inequality

In this paper, by using the Euler-Maclaurin expansion for the Riemann-$zeta$ function, we establish an inequality of a weight coefficient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.