SelectedWorks - Marion Scheepers

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Selected Works of Marion Scheepers

Distinguished Professor, Department of Mathematics

Dr. Marion Scheepers earned a Ph.D. in Mathematics from the University of Kansas, and joined the faculty of the Department of Mathematics at Boise State University in 1988. His research interests are in set theory (including combinatorics, game theory and Ramsey theory), cryptology, biomolecular computing paradigms, and computational algebra and number theory.
In recent years, with grant funding from the National Science Foundation, Dr. Scheepers has collaborated with researchers from the University of Witten-Herdecke in Germany, and the Boise State Department of Biological Sciences to study biological encryption mechanisms in certain single cell organisms. He hopes that this research can help pave the way for more interdisciplinary opportunities for students. Additionally, in 2012 Dr. Scheepers was honored as a Distinguished Professor in Mathematics. This title constitutes one of the highest honors that can be given to a faculty member at Boise State and is reserved for a small number who have made major contributions to their academic disciplines.

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About Marion Scheepers

Dr. Marion Scheepers earned a Ph.D. in Mathematics from the University of Kansas, and joined the faculty of the Department of Mathematics at Boise State University in 1988. His research interests are in set theory (including combinatorics, game theory and Ramsey theory), cryptology, biomolecular computing paradigms, and computational algebra and number theory.
In recent years, with grant funding from the National Science Foundation, Dr. Scheepers has collaborated with researchers from the University of Witten-Herdecke in Germany, and the Boise State Department of Biological Sciences to study biological encryption mechanisms in certain single cell organisms. He hopes that this research can help pave the way for more interdisciplinary opportunities for students. Additionally, in 2012 Dr. Scheepers was honored as a Distinguished Professor in Mathematics. This title constitutes one of the highest honors that can be given to a faculty member at Boise State and is reserved for a small number who have made major contributions to their academic disciplines.

Present	Distinguished Professor, Boise State University ‐ Department of Mathematics
Institution Organization Position Type Position Title Time Period to Options Current Position Affiliate my profile with this Institution

Mathematics and Set Theory

Set Theory, Game Theory, Cryptology, Elementary Number Theory, and Algorithmic Processes in Biology

2012 Distinguished Professor in Mathematics
1996 - Boise State University, Foundation Scholar Award for Research/Creative Activity
1993 - Boise State University, College of Arts and Sciences, Distinguished Research Award

Precalculus Algebra and Trigonometry
Calculus
Topology
Real Analysis
Complex Variables
Number Theory
Abstract Algebra I
Introduction to Mathematical Logic
Public Key Cryptography

E-mail: mscheepe@boisestate.edu

http://orcid.org/0000-0001-8037-8158

Articles (24)

Countable Dimensionality, a Game and the Haver Property (Liljana Babinkostova and Marion Scheepers) Proceedings of the American Mathematical Society (2021)

We characterize the countable dimensionality of metric spaces in terms of a game-theoretic version of a covering property of Haver, and conjecture a game-theoretic equivalent of Haver’s covering property for metric spaces.

Meager Sets, Games and Singular Cardinals (Liljana Babinkostova and Marion Scheepers) Topology & Its Applications (2020)

We show that a statement concerning the existence of winning strategies of limited memory in an infinite two-person topological game is equivalent to a weak version of the Singular Cardinals Hypothesis.

Quantifying CDS Sortability of Permutations by Strategic Pile Size (Marisa Gaetz, Bethany Flanagan, Marion Scheepers, et al.) Discrete Mathematics, Algorithms and Applications (2020)

The special purpose sorting operation, context directed swap (CDS), is an example of the block interchange sorting operation studied in prior work on permutation sorting. CDS has been postulated to model certain molecular sorting events ...

On a Hypothesis for ℵ0-Bounded Groups (Marion Scheepers) Topology and Its Applications (2019)

We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [6] holds while the classical Borel Conjecture fails.

Selective Versions of θ-Density (L. Babinkostova, B. A. Pansera and M. Scheepers) Topology and Its Applications (2019)

In [3] the authors initiate the study of selective versions of the notion of θ-separability in non-regular spaces. In this paper we continue this investigation by establishing connections between the familiar cardinal numbers arising in ...

Sorting Permutations: Games, Genomes, and Cycles (K. L. M. Adamyk, E. Holmes, G. R. Mayfield, et al.) Discrete Mathematics, Algorithms and Applications (2017)

Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting operations are considered ...

Baire Spaces and Infinite Games (Fred Galvin and Marion Scheepers) Archive for Mathematical Logic (2016)

It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The ...

Using Ciliate Operations to Construct Chromosome Phylogenies (Jacob L. Herlin, Anna Nelson and Marion Scheepers) Involve: A Journal of Mathematics (2016)

Whole genome sequencing has revealed several examples where genomes of different species are related by permutation. The number of certain types of rearrangements needed to transform one permuted list into another can measure the distance ...

Selective Games on Binary Relations (Rodrigo R. Dias and Marion Scheepers) Topology and Its Applications (2015)

We present a unified approach, based on dominating families in binary relations, for the study of topological properties defined in terms of selection principles and the games associated to them. Among other applications, this general ...

Remarks on Countable Tightness (Marion Scheepers) Topology and its Applications (2014)

Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize indestructibility of the Lindelöf ...

Weak Covering Properties and Selection Principles (L. Babinkostova, B. A. Pansera and Marion Scheepers) Topology and Its Applications (2013)

No convenient internal characterization of spaces that are productively Lindelöf is known. Perhaps the best general result known is Alsterʼs internal characterization, under the Continuum Hypothesis, of productively Lindelöf spaces which have a basis of ...

Borel's Conjecture in Topological Groups (Fred Galvin and Marion Scheepers) Journal of Symbolic Logic (2013)

We introduce a natural generalization of Borel's Conjecture. For each infinite cardinal number κ, let BCκ denote this generalization. Then BCℵ0 is equivalent to the classical Borel conjecture. Assuming the classical Borel conjecture, ¬BCℵ1 is ...

Weak Covering Properties and Infinite Games (L. Babinkostova, B. A. Pansera and M. Scheepers) Topology and its Applications (2012)

We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game. We use ...

Creating and Implementing Cloud-Based Simulations to Enhance a Multivariable Calculus Course (Joseph Guarino, Seung Youn Chyung, Charles Adams, et al.) Computers in Education Journal (2011)

A Cloud resource at Boise State University was used to enhance a large section of Multivariable and Vector Calculus (MATH 275) taken by engineering majors. This section was developed to deal with rapidly-increasing engineering enrollment. ...

Rothberger Bounded Groups and Ramsey Theory (Marion Scheepers) Topology and its Applications (2011)

We show that: (1) Rothberger bounded subgroups of σ-compact groups are characterized by Ramseyan partition relations (Corollary 4). (2) For each uncountable cardinal κ there is a T0 topological group of cardinality κ such that ...

Gerlits and Function Spaces (Marion Scheepers) Studia Scientiarum Mathematicarum Hungarica (2010)

János Gerlits died unexpectedly in 2008. In this paper we attempt to make a small tribute to his very powerful mathematical legacy by describing the emerging impact of two ideas, γ-spaces and Gerlits-Nagy spaces, from ...

Lindelöf Indestructibility, Topological Games and Selection Principles (Marion Scheepers and Franklin D. Tall) Fundamenta Mathematicae (2010)

Arhangel'skii proved that if a first countable Hausdorff space is Lindelöf, then its cardinality is at most 2 א‎0. Such a clean upper bound for Lindelöf spaces in the larger class of spaces whose points ...

Measurable Cardinals and the Cardinality of Lindelöf Spaces (Marion Scheepers) Topology and its Applications (2010)

We obtain from the consistency of the existence of a measurable cardinal the consistency of "small" upper bounds on the cardinality of a large class of Lindelöf spaces whose singletons are G δ sets.

Weakly Infinite Dimensional Subsets of RN (Liljana Babinkostova and Marion Scheepers) Topology and its Applications (2010)

The Continuum Hypothesis implies an Erdö-Sierpiński like duality between the ideal of first category subsets of ℝℕ, and the ideal of countable dimensional subsets of ℝℕ. The algebraic sum of a Hurewicz subset - a ...

Partition Relations for Hurewicz-Type Selection Hypotheses (Nadav Samet, Marion Scheepers and Boaz Tsaban) Topology and its Applications (2009)

We give a general method to reduce Hurewicz-type selection hypotheses into standard ones. The method covers the known results of this kind and gives some new ones. Building on that, we show how to derive ...

Rothberger's Property in All Finite Powers (Marion Scheepers) Topology and its Applications (2008)

A space X has the Rothberger property in all finite powers if, and only if, its collection of ω-covers has Ramseyan properties.

Combinatorics of Open Covers VI: Selectors for Sequences of Dense Sets (Marion Scheepers) Quaestiones Mathematicae (1999)

We consider the following two selection principles for topological spaces: [Principle 1:] { For each sequence of dense subsets, there is a sequence of points from the space, the n-th point coming from the n-th ...

Combinatorics of Open Covers (III): Games, Cp(X) (Marion Scheepers) Fundamenta Mathematicae (1997)

Some of the covering properties of spaces as defined in Parts I and II are here characterized by games. These results, applied to function spaces Cp(X) of countable tightness, give new characterizations of countable fan ...

Combinatorics of Open Covers (I): Ramsey Theory (Marion Scheepers) Topology and its Applications (1996)

We study several schemas for generating from one sort of open cover of a topological space a second sort of open cover. Some of these schemas come from classical literature, others are borrowed from the ...

Set Theory and Its Applications: Annual Boise Extravaganza in Set Theory, 1995--2010, Boise, Idaho (Liljana Babinkostova, Andrés Caicedo, S. Geschke, et al.) Faculty & Staff Authored Books (2011)

This book consists of several survey and research papers covering a wide range of topics in active areas of set theory and set theoretic topology. Some of the articles present, for the first time in ...