Klee-Phelps convex groupoids
-
James F. Peters
,
Mehmet A. Öztürk
and
Mustafa Uçkun
Abstract
We prove that a pair of proximal Klee-Phelps convex groupoids A(∘), B(∘) in a finite-dimensional normed linear space E are normed proximal, i.e., A(∘) δB(∘) if and only if the groupoids are normed proximal. In addition, we prove that the groupoid neighbourhood Nz(∘) ⊆ Sz(∘) is convex in E if and only if Nz(∘) = Sz(∘).
The research has been supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) Scientific Human Resources Development (BIDEB) under grant no: 2221-1059B211402463 and Natural Sciences & Engineering Research Council of Canada (NSERC) discovery grant 185986.
References
[1] Clifford, A. H.—Preston, G. B.: The Algebraic Theory of Semigroups I, Amer. Math. Soc., Providence, RI, 1964, MR0132791.Search in Google Scholar
[2] Di Concilio, A.: Proximity: A powerful tool in extension theory, function spaces, hyper-spaces, Boolean algebras and point-free geometry, Contemp. Math. 486 (2009), 89–114, MR2521943.10.1090/conm/486/09508Search in Google Scholar
[3] Klee, V. L.: A characterization of convex sets, Amer. Math. Monthly, 56 (1949), 247–249, MR0029519.10.2307/2304766Search in Google Scholar
[4] Naimpally, S. A.—Peters, J. F.: Topology with Applications. Topological Spaces Via Near and Far, World Scientific, Singapore, 2013, MR3075111, Zbl1295.68010.10.1142/8501Search in Google Scholar
[5] Peters, J. F.—Naimpally, S. A.: Applications of near sets, Notices Amer. Math. Soc. 59 (2012), 536–542, MR2951956.10.1090/noti817Search in Google Scholar
[6] Phelps, R. R.: Convex sets and nearest points, Proc. Amer. Math. Soc. 8 (1957), 790–797, MR0087897.10.1090/S0002-9939-1957-0087897-7Search in Google Scholar
[7] Čech, E.: Topological Spaces, revised edition by Z. Frolík and M. Katětov, John Wiley & Sons, London, 1966, MR0104205.Search in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- 10.1515/ms-2015-0200
- Zero-divisor graphs of lower dismantlable lattices I
- Some results on the intersection graph of submodules of a module
- Class number parities of compositum of quadratic function fields
- Examples of beurling prime systems
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Connection between multiplication theorem for Bernoulli polynomials and first factor
- On permutational invariance of the metric discrepancy results
- Evaluation of sums containing triple aerated generalized Fibonomial coefficients
- Linear algebraic proof of Wigner theorem and its consequences
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- Groups with the same complex group algebras as some extensions of psl(2, pn)
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- On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
- Weak interpolation for the lipschitz class
- Generalized Padé approximants for plane condenser and distribution of points
- Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
- Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
- Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
- Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
- On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
- Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
- Semi-equivelar maps on the torus and the Klein bottle with few vertices
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