Introduction (Proof)

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Epicurean Ethics in Horace: The Psychology of Satire, 2018

This is the first chapter of my 2018 monograph. I plan to upload the actual published version soon!

Lingua Aegyptia, 2021

pre-print, details may have changed in the printed paper

arXiv (Cornell University), 2018

We shorten the proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.

Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1988

2018

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis.

Journal of Algebra, 1973

2017

In:The Mamluk-Ottoman Transition: Continuity and Change in Egypt and Bilād al-Shām in the Sixteenth Century, ed. by Stephan Conermann /Gül Şen (Goettingen: Bonn University Press at V & R unipress, 2017), pp. 13-32 [Please consult the published version for correct page numbers]

2016

Let P be an open filter base for a filter F on X. We denote by C P (X) (C ∞P (X)) the set of all functions f ∈ C(X) where Z(f) ({x : |f (x)| < 1 n }) contains an element of P. First, we observe that every proper subrings in the sense of Acharyya and Ghosh (Topology Proc. 2010) has such form and vice versa. After wards, we generalize some well known theorems about C K (X), C ψ (X) and C ∞ (X) for C P (X) and C ∞P (X). We observe that C ∞P (X) may not be an ideal of C(X). It is shown that C ∞P (X) is an ideal of C(X) and for each F ∈ F , X \ F is bounded if and only if the set of non-cluster points of the filter F is bounded. By this result, we investigate topological spaces for which C ∞P (X) is an ideal of C(X) whenever P={A X: A is open and X \ A is bounded } (resp., P={A X: X \ A is finite }). Moreover, we prove that C P (X) is an essential (resp., free) ideal if and only if the set {V : V is open and X \ V ∈ F } is a π-base for X (resp., F has no cluster point). Finally, the filter F for which C ∞P (X) is a regular ring (resp., z-ideal) is characterized.

Introduction to the Topoi's special issue "Inferences and proofs", edited by Crocco G and Piccolomini d'Aragona A.