If a finite group G acts freely and simplicially on a complex homotopy equivalent to a sphere S, then G has periodic Tate cohomology: H (G;Z) ∼= H (G;Z) for all i > 0. Swan proved in [26] that this condition was also sufficient. For free topological actions on S itself, the first additional restriction is: Theorem. [19] A finite dihedral group does not act freely and topologically on S. Milnor’...

We prove that Thompson’s group F (n) is not minimally almost convex with respect to the standard finite generating set. A group G with Cayley graph Γ is not minimally almost convex if for arbitrarily large values of m there exist elements g, h ∈ Bm such that dΓ(g, h) = 2 and dBm (g, h) = 2m. (Here Bm is the ball of radius m centered at the identity.) We use tree-pair diagrams to represent eleme...

We obtain a sucint and nesessery theoreoms simple for compactness andweakly compactness of the best approximate sets by closed unit balls. Also weconsider relations Kadec-Klee property and shur property with this objects.These theorems are extend of papers mohebi and Narayana.

we show that in {bf zf} set theory without choice, the ultrafilter mbox{principle} ({bf up}) is equivalent to several compactness theorems for alexandroff discrete spaces and to rudin's lemma, a basic tool in topology and the theory of quasi-continuous domains. important consequences of rudin's lemma are various lift lemmas, saying that certain properties of posets are inherited by th...

This note provides an unbiased estimator for the absolute S-Gini and an almost unbiased estimator for the relative S-Gini for integer parameter values. Simulations indicate that these estimators perform considerably better then the usual estimators, especially for small sample sizes. 1 The absolute and relative S-gini indices Assume that income is distributed according to a continuous and diffe...

In this paper, we introduce soft complete continuity as a strong form of and continuity. Several characterizations, compositions, restriction theorems are obtained. Moreover, several preservation regarding compactness, Lindelofness, connectedness, regularity, normality, almost mild near paracompactness, metacompactness addition to these, the study deals with correlation between our new concepts...

L is a continuous function from R× into X and f is a continuous function from R to X . The theory of functional differential equations with infinite delay has been developed by several authors. The fundamental task of that kind of equations is the choice of phase space . Since the history function t→ ut is not continuous in general if u : (−∞,T] → X is continuous (where T > 0). The paper [9] co...

Given two finite sets of integers S ⊆ N \ {0} and D ⊆ N \ {0, 1}, the impartial combinatorial game i-Mark(S,D) is played on a heap of tokens. From a heap of n tokens, each player can move either to a heap of n − s tokens for some s ∈ S, or to a heap of n/d tokens for some d ∈ D if d divides n. Such games can be considered as an integral variant of Mark-type games, introduced by Elwyn Berlekamp ...

Co-author: Lúıs Castro We will present a study of the Fredholm property for matrix Wiener-Hopf plus/minus Hankel operators with semi-almost periodic Fourier symbols. The Fredholm property will be described based on certain factorizations of the representatives at infinity of the original symbols, and on the geometrical mean values of the corresponding factors. The Fredholm indices of those oper...