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991.
《Quaestiones Mathematicae》2013,36(1):63-78
Abstract An adaptation of a theorem by Herrlich [5] shows that every initially structured category A can be fully embedded in a topological category AC, which is, in fact, a MacNeille completion of A. It is then shown that A is Cartesian closed if and only if AC is. Also developed is the notion of a Cartesian closed initially structured (CCIS) hull of a category. The theory of the CCIS hull is analogous to that of the Cartesian closed topological (CCT) hull. It is proved that a category has a CCT hull-if and only if it has a CCIS hull; and this allows the list of conditions equivalent to the existence of a CCT hull to be supplemented. Examples are given, drawn mainly from the various categories of binary relations. 相似文献
992.
993.
《Quaestiones Mathematicae》2013,36(3-4):219-234
Abstract For a unital module V over a commutative ring R, let C denote the collection of cyclic submodules. The ring ?R(V;C) = {f ε EndR V |f(C) ?C, ?C εR (V;C) has been the object of several recent studies in which the structure of ?R(V;C) is related to the triple (V, R,C). Here we introduce a new ring HR(V;C) containing ?(V;C) and investigate its structure in terms of the parameters (V, R, C). 相似文献
994.
995.
996.
《Quaestiones Mathematicae》2013,36(5):673-685
AbstractFor a given d-dimensional polyhedral complex Δ and a given degree k, we consider the vector space of piecewise polynomial functions on Δ of degree at most k with a different smoothness condition on each pair of adjacent d-faces of Δ. This is a finite dimensional vector space. The fundamental problem in Approximation Theory is to compute the dimension of this vector space. It is known that the dimension is given by a polynomial for sufficiently large k via commutative algebra. By using the technique of McDonald and Schenck [3] and extending their result to a plane polyhedral complex Δ with varying smoothness conditions, we determine this polynomial. This gives a complete answer for the dimension. At the end we discuss some examples through this technique. 相似文献
997.
《Quaestiones Mathematicae》2013,36(5):593-604
AbstractLet X be a topological space and Cc(X) be the functionally countable subalgbera of C(X). We call X to be a countably uniform closed-space, briefly, a CU C-space, if Cc(X) is closed under uniform convergence. We investigate that countably uniform closedness need not closed under finite intersection and infinite product. It is shown that if X is a countable union of quasi-components, then X is a CU C-space. We characterize Cc-embedding and also -embedding in CU C-spaces. A subset S of X is called Zc-embedded, if each Z ∈ Zc(S) is the restriction of a zero-set of Zc(X). It is observed that in a zero-dimensional CU C-space, each Lindelöf subspae is Zc-embedded. Moreover, it is shown that in CU C-spaces, each Lindelöf subspace is Cc-embedded if and only if it is c-completely separated from each zero-set, which is disjoint from it. Also in latter spaces, it is observed that for each S ? X, Cc-embedding, -embedding and Zc-embedding coincide, when S belongs to Zc(X) or it is a c-pseudocompact space. Finally, when X is both a CU C-space and a CP-space, then each Zc-embedded subspace is Cc-embedded (-embedded) in X. 相似文献
998.
《Quaestiones Mathematicae》2013,36(7):903-916
AbstractUsing the definition of algebraic travelling wave solution for general 2-th order differential equations given in [9], we provide the only possible algebraic travelling wave solutions for the celebrated generalized Burgers-Fisher equation. 相似文献
999.
《Quaestiones Mathematicae》2013,36(4):449-456
Abstract In this paper we introduce some new double sequence spaces of fuzzy numbers using Orlicz function and also we examine that if a sequence of fuzzy numbers is double strongly convergent with respect to an Orlicz function then it is double statistical convergent. 相似文献
1000.
《Quaestiones Mathematicae》2013,36(2):265-274
We impose a condition on a commutative regular Fréchet algebra (A, (pm )) to ensure that A/kerpm is a Fréchet Q-algebra. This implies that if θ is an n-homomorphism on certain Fréchet algebras (A, (pm )) into semisimple commutative Fréchet algebras (B,(qm)) such that θ(kerpm) ? kerqm, for large enough m, then θ is continuous. We also show that if A is a Fréchet Q-algebra, B is a semisimple Fréchet algebra, θ: A → B is a dense range n-homomorphism such that θ(A) is factorizable, and the spectral radius vB is continuous on the separating space (θ), then θ is automatically continuous. 相似文献