Applied General Topology - Vol 15, No 2 (2014)https://riunet.upv.es:443/handle/10251/436082024-05-26T09:14:51Z2024-05-26T09:14:51ZSubgroups of paratopological groups and feebly compact groupsFernández, ManuelTkachenko, Mikhail G.https://riunet.upv.es:443/handle/10251/436312023-11-21T11:47:23Z2014-10-28T07:51:02ZSubgroups of paratopological groups and feebly compact groups
Fernández, Manuel; Tkachenko, Mikhail G.
[EN] It is shown that if all countable subgroups of a semitopological group G are precompact, then G is also precompact and that the closure of an arbitrary subgroup of G is again a subgroup. We present a general method of refining the topology of a given commutative paratopological group G such that the group G with the finer topology, say, σ is again a paratopological group containing a subgroup whose closure in (G, σ) is not a subgroup.
It is also proved that a feebly compact paratopological group H is perfectly k-normal and that every Gδ-dense subspace of H is feebly compact.
2014-10-28T07:51:02ZRadicals in the class of compact right topological ringsUrsul, MihailTripe, Adelahttps://riunet.upv.es:443/handle/10251/436302023-11-21T11:47:23Z2014-10-28T07:45:14ZRadicals in the class of compact right topological rings
Ursul, Mihail; Tripe, Adela
[EN] We construct in this article three radicals in the class of compact right topological rings. We prove also that a simple left Noetherian compact right topological ring is finite.
2014-10-28T07:45:14ZApproximation in different smoothness spaces with the RAFU methodCorbacho Cortés, Eduardohttps://riunet.upv.es:443/handle/10251/436292023-11-21T11:47:23Z2014-10-28T07:36:45ZApproximation in different smoothness spaces with the RAFU method
Corbacho Cortés, Eduardo
[EN] The RAFU method is an original and unknown approximation procedure we can use in Approximation Theory. We know that the RAFU method provides a linear space uniformly dense in C[a,b] by using some separation conditions. In this work, we will show we can employ the RAFU method to approximate functions of C0(R) and C00(R), Riemann integrable functions, Lebesgue integrable functions, functions of Lp[a,b] and Lp(R), 1≤p<¥ and measurable functions. Moreover, Riemann integrals can be approximated by the integrals of the functions that the RAFU method provides.
2014-10-28T07:36:45ZComputational topology for approximations of knotsLi, JiPeters, T. J.Jordan, K. E.https://riunet.upv.es:443/handle/10251/436282023-11-21T11:47:24Z2014-10-28T07:34:59ZComputational topology for approximations of knots
Li, Ji; Peters, T. J.; Jordan, K. E.
[EN] The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding:Hausdorff distance, anda sum of total curvature and derivative.High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern. Subdivision can produce PL approximations for a given B\'ezier curve, fulfilling the above two conditions. The primary contributions are: (i) a priori bounds on the number of subdivision iterations sufficient to achieve a PL approximation that is ambient isotopic to the original B\'ezier curve, and (ii) improved iteration bounds over those previously established.
2014-10-28T07:34:59ZFunction lattices and compactificationsAlaste, Tomi Matiashttps://riunet.upv.es:443/handle/10251/436272023-11-21T11:47:24Z2014-10-28T07:32:23ZFunction lattices and compactifications
Alaste, Tomi Matias
[EN] Let F be a lattice of real-valued functions on a non-empty set X such that F contains the constant functions. Using certain filters on X determined by F, we construct a compact Hausdorff topological space δX with the property that every bounded member of F extends to δX and these extensions form a dense subspace of C(δX). If A is any C*-subalgebra of ℓ∞(X) containing the constant functions, then our construction gives a representation of the spectrum of A as a space of filters on X.
2014-10-28T07:32:23ZLifting Dynamical Properties to HyperspacesMasood, DaniaSingh, Poojahttps://riunet.upv.es:443/handle/10251/436192023-11-21T11:47:24Z2014-10-27T16:58:06ZLifting Dynamical Properties to Hyperspaces
Masood, Dania; Singh, Pooja
[EN] For a dynamical system (X,f), the passage of various dynamical properties such as transitivity, total transitivity, weakly mixing, mixing, topological exactness, topological conjugacy, to the hyperspace C(X) of X consisting of nonempty closed connected subsets of X, and also to the hyperspace suspension HS(X) of X, have been considered and studied.
2014-10-27T16:58:06ZOn the topology of the chain recurrent set of a dynamical systemAhmadi, Seyyed Alirezahttps://riunet.upv.es:443/handle/10251/436182023-11-21T11:47:24Z2014-10-27T16:55:27ZOn the topology of the chain recurrent set of a dynamical system
Ahmadi, Seyyed Alireza
[EN] In this paper we associate a pseudo-metric to a dynamical system on a compact metric space. We show that this pseudo-metric is identically zero if and only if the system is chain transitive. If we associate this pseudo-metric to the identity map, then we can present a characterization for connected and totally disconnected metric spaces.
2014-10-27T16:55:27ZR-spaces and closedness/completeness of certain function spaces in the topology of uniform convergenceKohli, J. K.Singh, Davinderhttps://riunet.upv.es:443/handle/10251/436172023-11-21T11:47:23Z2014-10-27T16:52:54ZR-spaces and closedness/completeness of certain function spaces in the topology of uniform convergence
Kohli, J. K.; Singh, Davinder
[EN] It is shown that the notion of an − cl R space (Demonstratio Math. 46(1) (2013), 229-244) fits well as a separation axiom between zero dimensionality and − 0 R spaces. Basic properties of − cl R spaces are studied and their place in the hierarchy of separation axioms that already exist in the literature is elaborated. The category of − cl R spaces and continuous maps constitutes a full isomorphism closed, monoreflective (epireflective) subcategory of TOP. The function space cl R (X, Y) of all − cl R supercontinuous functions from a space X into a uniform space Y is shown to be closed in the topology of uniform convergence. This strengthens and extends certain results in the literature (Demonstratio Math. 45(4) (2012), 947-952).
2014-10-27T16:52:54ZThe classical ring of quotients of $C_c(X)$Bhattacharjee, PapiyaKnox, Michelle L.McGovern, Warren Wm.https://riunet.upv.es:443/handle/10251/436142023-11-21T11:47:24Z2014-10-27T16:44:53ZThe classical ring of quotients of $C_c(X)$
Bhattacharjee, Papiya; Knox, Michelle L.; McGovern, Warren Wm.
[EN] We construct the classical ring of quotients of the algebra of continuous real-valued functions with countable range. Our construction is a slight modification of the construction given in [M. Ghadermazi, O.A.S. Karamzadeh, and M. Namdari, On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova, to appear]. Dowker's example shows that the two constructions can be different.
2014-10-27T16:44:53ZAsymptotic structures of cardinalsPetrenko, OleksandrProtasov, Igor V.Slobodianiuk, Sergiihttps://riunet.upv.es:443/handle/10251/436132023-11-21T11:47:24Z2014-10-27T16:39:21ZAsymptotic structures of cardinals
Petrenko, Oleksandr; Protasov, Igor V.; Slobodianiuk, Sergii
[EN] A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F) can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define F using a natural order structure on k. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans.
2014-10-27T16:39:21Z