Advanced Topology and Set Theory

(integrands of multiple integrals) that are independent, in the large, modulo the derived forms. The geometrical method of approach has been extended to compact metric spaces by Vietoris' and to still more general spaces by tech.2 Moreover, this branch of the theory has been very greatly perfected by the introduction…

In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set-valued mapping T ∗ T^* of a metric tree M M with convex values has a selection T : M → M T: M\right…

• ALPEREN AKSOY

Let X be a first countable Hausdorff topological group. The limit of a sequence in X defines a function denoted by lim from the set of all convergent sequences to X. This notion has been modified by Connor and Grosse-Erdmann for real functions by replacing lim with an arbitrary linear functional G defined on a linear…

• TUNÇAR ŞAHAN

(1994). Variations on Wolstenholme's Theorem. The American Mathematical Monthly: Vol. 101, No. 10, pp. 1001-1004.

It is proved that the automorphism group of any non-abelian free group F is complete. The key technical step in the proof is that the set of all conjugations by powers of primitive elements is first-order parameter-free definable in the group Aut(F).

A representation G U (n) of degree n has fixity equal to the smallest integer f such that the induced action of G on U (n)/U (n -f -1) is free. Using bundle theory we show that if G admits a representation of fixity one, then it acts freely and smoothly on S 2n-1 S 4n-5 . We use this to prove that a finite p-group (fo…

• ÖZGÜN ÜNLÜ

This paper concerns rigidity of the mapping class groups. It is shown that any homomorphism ϕ : Modg → Modh between mapping class groups of closed orientable surfaces with distinct genera g > h is trivial if g ⩾ 3, and has finite cyclic image for all g ⩾ 1. Some implications are drawn for more general homomorphs of th…

• MUSTAFA KORKMAZ

This paper concerns rigidity of the mapping class groups. It is shown that any homomorphism ϕ : Modg → Modh between mapping class groups of closed orientable surfaces with distinct genera g > h is trivial if g ⩾ 3, and has finite cyclic image for all g ⩾ 1. Some implications are drawn for more general homomorphs of th…

• MUSTAFA KORKMAZ

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• AYHAN GÜNAYDIN

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• AHMET SİNAN ÇEVİK