Abstract The Reeb space of a continuous function is the connected components level sets. In this paper, we first prove that smooth on closed manifold with finitely many critical values has structure finite graph without loops. We also show an arbitrary loops can be realized as certain values, where corresponding sets preassigned. Finally, map to induces epimorphism between fundamental groups id...

Here we investigate algebras associated with algebraizations of (variants of) first-order logic and of multi-modal logics. We will use the notation of the fundamental textbook Henkin Monk Tarski [8] (Parts I, II) of algebraic logic, but we will try to keep the present note self-contained. In a way, this work is a continuation of [23] but we do not assume familiarity with that work. For a class ...

Proposition 1. (Grunewald [5, Proposition B]) Let F be a free group of rank k ≥ 2, generated by {s1, . . . , sk}. Let r1, . . . , rm be words over {s1, . . . , sk} ±1 and R their normal closure 〈〈r1, . . . , rm〉〉F in F . Let H be the group with presentation 〈s1, . . . , sk | r1, . . . , rm〉 and φ the canonical epimorphism φ : F → H ∼= F/R. Let F be a free group of rank k generated by {t1, . . ....

For an associative ring R, let P be an R-module with S = EndR(P). C. Menini and A. Orsatti posed the question of when the related functor HomR(P, −) (with left adjoint P ⊗S −) induces an equivalence between a subcategory of R M closed under factor modules and a subcategory of S M closed under submodules. They observed that this is precisely the case if the unit of the adjunction is an epimorphi...

such that f(g(a)) = a for all a ∈ L. Projective lattices are characterized in [3] by four conditions. This talk will discuss two of them that are of current interest. If g in (2) is only required to be order-preserving, it is called an isotone section of the epimorphism (1). We will characterize which lattices L have an isotope section for every epimorphism (1). We will use this to characterize...

Our aim is to give an explicit description of the Arens-Michael envelope for universal enveloping algebra a finite-dimensional nilpotent complex Lie algebra. It turns out that belongs class completions introduced by R.~Goodman in 70s. To find precise form this we preliminary characterize set holomorphic functions exponential type on simply connected group. This approach leads unexpected connect...

Abstract We study homotopy epimorphisms and covers formulated in terms of derived Tate’s acyclicity for commutative $C^*$-algebras algebras continuous functions valued non-Archimedean fields. prove that a epimorphism between precisely corresponds to closed immersion the compact Hausdorff topological spaces associated with them cover $C^*$-algebra space it by immersions admitting finite subcover...

‎given an integer $n$‎, ‎we denote by $mathfrak b_n$ and $mathfrak c_n$ the classes of all groups $g$ for which the map $phi_{n}:gmapsto g^n$ is a monomorphism and an epimorphism of $g$‎, ‎respectively‎. ‎in this paper we give a characterization for groups in $mathfrak b_n$ and for groups in $mathfrak c_n$‎. ‎we also obtain an arithmetic description of the set of all integers $n$ such that a gr...

This note gives a complete characterization of when the ordinal sum of two lattices (the lattice obtained by placing the second lattice on top of the first) is projective. This characterization applies not only to the class of all lattices, but to any variety of lattices, and in particular, to the class of distributive lattices. Lattices L with the property that every epimorphism onto L has an ...

For many decision problems on a finitely presented group G, we can quickly weed out negative solutions by using much quicker algorithms on an appropriately chosen quotient group G/K of G. However, the behavior of such “quotient tests” can be sometimes paradoxical. In this paper, we analyze a few simple case studies of quotient tests for the classical identity, word, conjugacy problems in groups...