soranzo units.it, tironi units.it The problem of finding compact sequential spaces of arbitrary o... more soranzo units.it, tironi units.it The problem of finding compact sequential spaces of arbitrary order is presented and its dependence on the assumptions of the Theory of Sets is examined. In particular several constructions due to Baškirov, Kannan and Dow are compared. (Joint with Alessandro Soranzo.)
y Abstract. The notion of PBS-sublattice is introduced and, using it, a simplication of the resul... more y Abstract. The notion of PBS-sublattice is introduced and, using it, a simplication of the results of (6) and of some results of (5) is ob- tained. Two propositions concerning Wallman-type compactications are presented as well.
Abstract. A new cardinal invariant, the quasi-character, is introduced and some of its interestin... more Abstract. A new cardinal invariant, the quasi-character, is introduced and some of its interesting properties are studied, particula r ly in the class of chain-net or pseudo-radial spaces. Main results are that the quasi-character coincides with the tightness for pseudo-...
In this paper the problem is posed of the prescription of the so-called Boltzmann-Grad (BG) limit... more In this paper the problem is posed of the prescription of the so-called Boltzmann-Grad (BG) limit ($\mathcal{L}_{BG}$) for the $N-$body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. The statistical description is couched in terms of the Master kinetic equation, i.e., the kinetic equation which realizes the axiomatic "\textit{ab initio}" approach to the classical statistical mechanics of finite hard-sphere systems recently developed (Tessarotto \textit{et al.}, 2013-2017). The issue addressed here concerns the prescription of the BG-limit operator and specifically the non-commutative property of $\mathcal{L}_{BG}$ with the free-streaming operator which enters the same kinetic equation.\ It is shown\ that the form of the resulting limit equation remains in principle non-unique, its precise realization depending critically on the way the action of the same operator is prescribed. Implications for the global pre...
The concept of essential sequence and essential space is given within the class of pseudoradial s... more The concept of essential sequence and essential space is given within the class of pseudoradial spaces. This concept tries to clarify the behaviour of convergent (long) sequences. Various examples and implications are proved among classes of pseudoradial (and radial, semiradial, almost radial) essential spaces. It is shown that essentially radial spaces are the same as pseudoradial Whyburn spaces. A list of open problems is given.
L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova... more L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Abstract We consider the notion of strongly pseudoradial space. Among other things, we examine it... more Abstract We consider the notion of strongly pseudoradial space. Among other things, we examine its relation with various similar notions, including the weak Whyburn property. Our investigation will suggest several interesting questions.
In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological... more In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological space, similar to the Tychonoff topology but weaker than it. In 1998, G. Dimov and D. Vakarelov used a generalized version of this new topology, calling it Tychonoff-type topology. The present paper is devoted to a detailed study of Tychonoff-type topologies on an arbitrary family M of subsets of a set X. When M contains all singletons, a description of all Tychonoff-type topologies O on M is given. The continuous maps of a special form between spaces of the type (M,O) are described in an isomorphism theorem. The problem of commutability between hyperspaces and subspaces with respect to a Tychonoff-type topology} is investigated as well. Some topological properties of the hyperspaces (M,O) with Tychonoff-type topologies O are briefly discussed.
In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological... more In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological space, similar to the Tychonoff topology but weaker than it. In 1998, G. Dimov and D. Vakarelov used a generalized version of this new topology, calling it Tychonoff-type topology. The present paper is devoted to a detailed study of Tychonoff-type topologies on an arbitrary family M of subsets of a set X. When M contains all singletons, a description of all Tychonoff-type topologies O on M is given. The continuous maps of a special form between spaces of the type (M,O) are described in an isomorphism theorem. The problem of commutability between hyperspaces and subspaces with respect to a Tychonoff-type topology} is investigated as well. Some topological properties of the hyperspaces (M,O) with Tychonoff-type topologies O are briefly discussed.
soranzo units.it, tironi units.it The problem of finding compact sequential spaces of arbitrary o... more soranzo units.it, tironi units.it The problem of finding compact sequential spaces of arbitrary order is presented and its dependence on the assumptions of the Theory of Sets is examined. In particular several constructions due to Baškirov, Kannan and Dow are compared. (Joint with Alessandro Soranzo.)
y Abstract. The notion of PBS-sublattice is introduced and, using it, a simplication of the resul... more y Abstract. The notion of PBS-sublattice is introduced and, using it, a simplication of the results of (6) and of some results of (5) is ob- tained. Two propositions concerning Wallman-type compactications are presented as well.
Abstract. A new cardinal invariant, the quasi-character, is introduced and some of its interestin... more Abstract. A new cardinal invariant, the quasi-character, is introduced and some of its interesting properties are studied, particula r ly in the class of chain-net or pseudo-radial spaces. Main results are that the quasi-character coincides with the tightness for pseudo-...
In this paper the problem is posed of the prescription of the so-called Boltzmann-Grad (BG) limit... more In this paper the problem is posed of the prescription of the so-called Boltzmann-Grad (BG) limit ($\mathcal{L}_{BG}$) for the $N-$body system of smooth hard-spheres which undergo unary, binary as well as multiple elastic instantaneous collisions. The statistical description is couched in terms of the Master kinetic equation, i.e., the kinetic equation which realizes the axiomatic "\textit{ab initio}" approach to the classical statistical mechanics of finite hard-sphere systems recently developed (Tessarotto \textit{et al.}, 2013-2017). The issue addressed here concerns the prescription of the BG-limit operator and specifically the non-commutative property of $\mathcal{L}_{BG}$ with the free-streaming operator which enters the same kinetic equation.\ It is shown\ that the form of the resulting limit equation remains in principle non-unique, its precise realization depending critically on the way the action of the same operator is prescribed. Implications for the global pre...
The concept of essential sequence and essential space is given within the class of pseudoradial s... more The concept of essential sequence and essential space is given within the class of pseudoradial spaces. This concept tries to clarify the behaviour of convergent (long) sequences. Various examples and implications are proved among classes of pseudoradial (and radial, semiradial, almost radial) essential spaces. It is shown that essentially radial spaces are the same as pseudoradial Whyburn spaces. A list of open problems is given.
L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova... more L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Abstract We consider the notion of strongly pseudoradial space. Among other things, we examine it... more Abstract We consider the notion of strongly pseudoradial space. Among other things, we examine its relation with various similar notions, including the weak Whyburn property. Our investigation will suggest several interesting questions.
In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological... more In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological space, similar to the Tychonoff topology but weaker than it. In 1998, G. Dimov and D. Vakarelov used a generalized version of this new topology, calling it Tychonoff-type topology. The present paper is devoted to a detailed study of Tychonoff-type topologies on an arbitrary family M of subsets of a set X. When M contains all singletons, a description of all Tychonoff-type topologies O on M is given. The continuous maps of a special form between spaces of the type (M,O) are described in an isomorphism theorem. The problem of commutability between hyperspaces and subspaces with respect to a Tychonoff-type topology} is investigated as well. Some topological properties of the hyperspaces (M,O) with Tychonoff-type topologies O are briefly discussed.
In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological... more In 1975, M. M. Choban introduced a new topology on the set of all closed subsets of a topological space, similar to the Tychonoff topology but weaker than it. In 1998, G. Dimov and D. Vakarelov used a generalized version of this new topology, calling it Tychonoff-type topology. The present paper is devoted to a detailed study of Tychonoff-type topologies on an arbitrary family M of subsets of a set X. When M contains all singletons, a description of all Tychonoff-type topologies O on M is given. The continuous maps of a special form between spaces of the type (M,O) are described in an isomorphism theorem. The problem of commutability between hyperspaces and subspaces with respect to a Tychonoff-type topology} is investigated as well. Some topological properties of the hyperspaces (M,O) with Tychonoff-type topologies O are briefly discussed.
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