A characterization of the quotient proximity is given. It is used to find necessary and sufficient conditions for every proximity map on a space to be a topological quotient map. It is shown that a separated proximity space is compact iff every /7-map on X with separated range is a proximity quotient map. Introduction. In 1959 Katetov [3] introduced proximity quotient maps. They have since been...

Kollár’s conjecture states that a complex projective surface S with quotient singularities and with H(S, Q) = Q should be rational if its smooth part S is simply connected. We confirm the conjecture under the additional condition that the exceptional divisor in a minimal resolution of S has at most 3 components over each singular point of S.

Abstract Almost s s -mappings and almost compact mappings have been introduced studied. In this article, we continue to research some questions related the -images (resp., images) of metric spaces. The following results are obtained. (1) A space X X is a quotient image if only sequential having c</m:...

In 1966, Michael [11] introduced the concept of compact-covering maps. Since many important kinds of maps are compact-covering, such as closed maps on paracompact spaces, much work has been done to seek the characterizations of metric spaces under various compact-covering maps, for example, compact-covering (open) s-maps, pseudosequence-covering (quotient) s-maps, sequence-covering (quotient) s...

In his 1974 text, Commutative Ring Theory, Kaplansky states that among the examples of non-Dedekind Prüfer domains, the main ones are valuation domains, the ring of entire functions and the integral closure of a Prüfer domain in an algebraic extension of its quotient field [Kap74, p.72]. A similar list today would likely include Kronecker function rings, the ring of integervalued polynomials an...

Consider an involution T of the sphere S without fixed points. Is the quotient manifold S/T necessarily isomorphic to projective nspace? This question makes sense in three different categories. One can work either with topological manifolds and maps, with piecewise linear manifolds and maps, or with differentiable manifolds and maps. For n^3 the statement is known to be true (Livesay [6]). In t...

Given an affine algebraic variety V and a quantization Oq(V ) of its coordinate ring, it is conjectured that the primitive ideal space of Oq(V ) can be expressed as a topological quotient of V . Evidence in favor of this conjecture is discussed, and positive solutions for several types of varieties (obtained in joint work with E. S. Letzter) are described. In particular, explicit topological qu...

In this paper, all the monoids considered are commutative. If S is a monoid generated by {m1, . . . ,mn}, then S is isomorphic to a quotient monoid of N by the kernel congruence σ of the map φ : N → S, φ(k1, . . . , kn) = ∑n i=1 kimi. Under this setting, a finite presentation for S is a finite subset ρ of Nn×Nn such that the congruence generated by ρ is equal to σ. Rédei proves in [5] that ever...

Tujuan dari pendidikan kewirausahaan untuk anak usia dini yakni menjadikan peserta didik menjadi orang yang pandai, kreatif dan inovatif sekaligus memiliki jiwa pemberani, suka menerima tantangan, berani mengambil resiko tidak mudah pesimis. Penelitian dilakukan di PAUD TPQ Rochmatul Ummah Purwosari Kudus. Responden dalam penelitian ini adalah ada Kudus dengan tujuan memberikan inovasi kepada s...

We define and study the signature and higher signatures of the quotient space of an S-action on a closed oriented manifold.