On the topological structure of Mikusinski's operators
O. Hadžić (1971)
Matematički Vesnik
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O. Hadžić (1971)
Matematički Vesnik
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Bekkai Messirdi, Mohammed Hichem Mortad, Abdelhalim Azzouz, Ghouti Djellouli (2008)
Colloquium Mathematicae
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The purpose of this work is to give a topological condition for the usual product of two closed operators acting in a Hilbert space to be closed.
Chung-Chuan Chen, J. Alberto Conejero, Marko Kostić, Marina Murillo-Arcila (2017)
Open Mathematics
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We introduce several notions of linear dynamics for multivalued linear operators (MLO’s) between separable Fréchet spaces, such as hypercyclicity, topological transitivity, topologically mixing property, and Devaney chaos. We also consider the case of disjointness, in which any of these properties are simultaneously satisfied by several operators. We revisit some sufficient well-known computable criteria for determining those properties. The analysis of the dynamics of extensions of...
M. H. Castro, V. A. Menegatto, A. P. Peron (2012)
Colloquium Mathematicae
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We analyze some aspects of Mercer's theory when the integral operators act on L²(X,σ), where X is a first countable topological space and σ is a non-degenerate measure. We obtain results akin to the well-known Mercer's theorem and, under a positive definiteness assumption on the generating kernel of the operator, we also deduce series representations for the kernel, traceability of the operator and an integration formula to compute the trace. In this way, we upgrade considerably similar...
Nurettin Bağırmaz, İlhan İçen, Abdullah F. Özcan (2016)
Topological Algebra and its Applications
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The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups on an approximation space.
De Xue Zhang (2000)
Commentationes Mathematicae Universitatis Carolinae
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Let be a completely distributive lattice and a topological construct; a process is given in this paper to obtain a topological construct , called the tower extension of (indexed by ). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process...
J. Anusiak, K. P. Shum (1971)
Colloquium Mathematicae
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G. J. Michaelides (1975)
Colloquium Mathematicae
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P. Doyle (1975)
Fundamenta Mathematicae
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Aleksander V. Arhangel'skii, Miroslav Hušek (2001)
Commentationes Mathematicae Universitatis Carolinae
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The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group that is not Dieudonné complete one can find a Dieudonné complete group such that the Dieudonné completion of is not a topological group containing as a subgroup. Using Korovin’s construction of -dense orbits, we present some examples showing that some results on topological groups are not valid...
T. Nadzieja, J. Šiska (1988)
Applicationes Mathematicae
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