## About

21

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Introduction

Mark Bowron currently works at mathematrucker.com. Mark does research in General Topology. His current project is 'Kuratowski Closure-Complement Theorem'.

**Skills and Expertise**

Additional affiliations

Education

August 1984 - May 1986

October 1978 - May 1983

**University of Washington**

Field of study

- Mathematics

## Publications

Publications (21)

The Kuratowski monoid $\mathcal{K}$ is generated under operator composition by closure and complement in a nonempty topological space. It satisfies $2\leq|\mathcal{K}|\leq14$. The Gaida-Eremenko (or GE) monoid $\mathcal{KF}$ extends $\mathcal{K}$ by adding the boundary operator. It satisfies $4\leq|\mathcal{KF}|\leq34$. We show that when $|\mathcal...

English translation of Quelques notions fondamentales de l’Analysis Situs au point de vue de l’Algèbre de la Logique by Miron Zarycki (Some Fundamental Concepts of Topology in Terms of the Algebra of Logic) by Mark Bowron. A note by Zarycki on the frontier operator in connected spaces appears in the Appendix.

The author develops on a postulational basis the area of point-set topology concerning coherences and adherences. The postulates are those underlying the usual algebra of logic and three others which become familiar theorems when the undefined terms are given a particular (point-set topological) interpretation. These three postulates are shown to f...

Fréchet and others have taken properties of set concepts such as boundary, derived set, closure, etc. and deduced further properties of the resulting "abstract" sets, giving rise to theories of general spaces. For example, depending on which topological concepts are accepted as basic and which properties are selected as axioms, various different "t...

English translation of Kuratowski's 1922 paper. Reprinted with permission from the Polish Academy of Sciences.

Mathematical journal and contest problems from 1975-1979 arranged by subject. Includes author index.

In Pascal's Triangle, if you begin with one of the first five entries in a row and sum it with every fifth entry that follows in that row, the difference between any two such sums is always a Fibonacci number. Donald Knuth proposed this same problem as Problem 1621 in the April 2001 issue of Mathematics Magazine. See also: "Some Formulae for the Fi...

English translation of Числа Куратовского by А. В. Чагров (Kuratowski Numbers by A. V. Chagrov) by Mark Bowron.

Kuratowski (1922) proved that 14 is the largest number of distinct sets that can be obtained from an arbitrary subset in a topological space by repeatedly applying the closure and complement operations in any order. Zarycki (1927) showed that by repeatedly applying the complement and frontier operators to an arbitrary subset in a topological space,...

Kuratowski (1922) proved that 14 is the largest number of distinct sets that can be obtained from an arbitrary subset in a topological space by repeatedly applying the closure and complement operations in any order. The paper contains a generalization of this result to the case of closure spaces and discusses related combinatorial problems.

To verify the independence of the closure axioms, Kuratowski considered the following problem in [8] and [9, 48]: " How many different sets may be obtained from an arbitrary subset of a topological space by applying closure and complement to it in any order ? " Kuratowski showed that no more than 14 distinct sets can be obtained. Many variants of t...