The University of Dayton Department of Mathematics hosted the 32nd Summer Conference on Topology and Its Applications June 27–30, 2017. The conference featured five sessions, each with a plenary speaker and two semi-plenary speakers. The conference also featured a presentation by Kathryn Mann of the University of California, Berkeley, the recipient of the 2016 Mary Ellen Rudin Young Researchers Award.

The event received sponsorship from the National Science Foundation to provide financial assistance to students, early career mathematicians, and those without institutional support.
This collection includes abstracts and presentation slides for the research presented at the conference. Selected papers will be published in *Topology Proceedings*, ISSN 0146-4124.

Abstracts from conferences from 1995 to the present are available at the conference archive.

#### Conference Information

Conference Program, University of Dayton

#### Plenary Lectures

A Compact Minimal Space Whose Cartesian Square Is Not Minimal, Jan P. Boronski, Alex Clark, and Piotr Oprocha

Locally Compact Groups: Traditions and Trends, Karl Heinrich Hofmann, Wolfgang Herfort, and Francesco G. Russo

Order, Distance, Closure and Convergence: Reconciling Competing Fundamental Topological Concepts, Walter Tholen

Dense Subsets of Function Spaces with No Non-Trivial Convergent Sequences, Vladimir V. Tkachuk

#### Semi-plenary lectures

Classifying Matchbox Manifolds, Olga Lukina

Rigidity and Nonrigidity of Corona Algebras, Paul McKenney and Alessandro Vignati

Domains and Probability Measures: A Topological Retrospective, Michael Mislove

Topologically Homogeneous Continua, Isometrically Homogeneous Continua, and the Pseudo-Arc, Janusz Prajs

Topology and Order, Tom Richmond

On the Lindelöf Σ-Property and Some Related Conclusions, Reynaldo Rojas-Hernandez, Fidel Casarrubias-Segura, and Salvador Garcia-Ferreira

#### Topology + Algebra and Analysis

Quantale-Valued Gauge Groups and Approach Convergence Transformation Groups, T.M.G. Ahsanullah

On a Construction of Some Class of Metric Spaces, Dariusz Bugajewski

Generic Approximation and Interpolation by Entire Functions via Restriction of the Values of the Derivatives, Maxim R. Burke

Which Topological Groups Arise as Automorphism Groups of Locally Finite Graphs?, Xiao Chang and Paul Gartside

Compactly Supported Homeomorphisms as Long Direct Limits, Rafael Dahmen and Gábor Lukács

On the Tightness and Long Directed Limits of Free Topological Algebras, Gábor Lukács and Rafael Dahmen

Balanced and Functionally Balanced P-Groups, Menachem Shlossberg

Interpolation Sets in Compact Groups, Luis Tárrega, Salvador Hernandez, and Maria V. Ferrer

#### Topology + Asymmetric Structures

On Di-injective T0-Quasi-metric Spaces, Collins Amburo Agyingi

The Isbell-hull of an Asymmetrically Normed Space, Olivier Olela Otafudu, Jurie Conradie, and Hans-Peter Künzi

Enriched Topology and Asymmetry, Stephen Rodabaugh, Jeffrey T. Denniston, and Austin Melton

Relationships between Hereditary Sobriety, Sobriety, TD, T1, and Locally Hausdorff, Stephen Rodabaugh, Jeffrey T. Denniston, Austin Melton, and Jamal K. Tartir

On Quasi-Uniform Box Products, Hope Sabao and Olivier Olela Otafudu

#### Topology + Dynamics and Continuum Theory

A Trace Formula for Foliated Flows (working paper), Jesús A. Álvarez López, Yuri A. Kordyukov, and Eric Leichtnam

Entropy of Induced Continuum Dendrite Homeomorphisms, Jennyffer Bohorquez and Alexander Arbieto

Pseudo-Contractibility, Felix Capulín, Leonardo Juarez-Villa, and Fernando Orozco

Topology and Experimental Distinguishability, Gabriele Carcassi, Christine A. Aidala, David J. Baker, and Mark J. Greenfield

Liouville Numbers and One-sided Ergodic Hilbert Transformations, David Constantine and Joanna Furno

Hausdorff Dimension of Kuperberg Minimal Sets, Daniel Ingbretson

The Specification Property and Infinite Entropy for Certain Classes of Linear Operators, James Kelly, Will Brian, and Tim Tennant

Shift Maps and Their Variants on Inverse Limits with Set-Valued Functions, Judy Kennedy, Kazuhiro Kawamura, Van Nall, and Goran Erceg

Sequential Decreasing Strong Size Properties, Miguel A. Lara, Fernando Orozco, and Felix Capulín

Aperiodic Colorings and Dynamics, Ramon Barral Lijo and Jesús A. Álvarez López

Quotients of n-fold Hyperspaces, Sergio Macías and Javier Camargo

A New Class of Dendrites Having Unique Second Symmetric Product, David Maya, José G. Anaya, and Fernando Orozco Zitli

On Continua with Regular Non-abelian Self Covers, Mathew Timm

#### Topology + Foundations

Revelation of Nano Topology in Cech Rough Closure Spaces, V. Antonysamy, Llellis Thivagar, and Arockia Dasan

On Cohomological Dimensions of Remainders of Stone-Čech Compactifications, Vladimer Baladze

On Roitman's Principle for Box Products, Hector Alonso Barriga-Acosta

On the Chogoshvili Homology Theory of Continuous Maps of Compact Spaces, Anzor Beridze and Vladimer Baladze

On Cardinality Bounds Involving the Weak Lindelöf Degree and H-Closed Spaces, Nathan Carlson, Angelo Bella, and Jack Porter

Sequential Order of Compact Scattered Spaces, Alan Dow

Spaces with No S or L Subspaces, Joan Hart and Kenneth Kunen

Disjoint Infinity Borel Functions, Daniel Hathaway

Properties of Weak Domain Representable Spaces, Joe Mashburn

On the Axiomatic Systems of Steenrod Homology Theory of Compact Spaces, Leonard Mdzinarishvili and Anzor Beridze

Compactness via Adherence Dominators, Bhamini M. P. Nayar, Terrence A. Edwards, James E. Joseph, and Myung H. Kwack

Normal Images of a Product and Countably Paracompact Condensation, Jila Niknejad

Relationships between Topological Properties of X and Algebraic Properties of Intermediate Rings A(X), Joshua Sack

Some Applications of the Point-Open Subbase Game, David Guerrero Sanchez

Cohen Reals and the Sequential Order of Groups, Alexander Shibakov

Fiber Strong Shape Theory for Topological Spaces, Ruslan Tsinaridze and Vladimer Baladze

Some New Completeness Properties in Topological Spaces, Cetin Vural and Süleyman Önal

#### Topology + Geometry

On Product Stability of Asymptotic Property C, Gregory C. Bell and Andrzej Nagórko

Virtual Seifert Surfaces and Slice Obstructions For Knots in Thickened Surfaces, Micah Chrisman, Hans U. Boden, and Robin Gaudreau

Totally Geodesic Surfaces in Arithmetic Hyperbolic 3-Manifolds, Benjamin Linowitz and Jeffrey S. Meyer

Uncountably Many Quasi-Isometry Classes of Groups of Type FP, Ignat Soroko, Robert Kropholler, and Ian Leary

Extension Theorems for Large Scale Spaces via Neighbourhood Operators, Thomas Weighill and Jerzy Dydak

Lifting Homeomorphisms of Cyclic Branched Covers of the Sphere, Rebecca R. Winarski and Tyrone Ghaswala

#### Workshops

Entropy in Topological Groups, Part 1, Dikran Dikranjan

Entropy in Topological Groups, Part 2, Dikran Dikranjan