Research

• The finite product of connected linearly ordered sets cannot be embedded into the product of a smaller dimension., Topology Proceedings 66 (2025), 135-148(PDF)
• Brouwer's fixed-point theorem on the finite product of compact linearly ordered topological spaces, Topology and its Applications 362 (2025), Paper No. 109221, 14pp(DOI)
• Perfectly normal nonrealcompact spaces under Martin's Maximum, Mathematical Logic Quarterly 70 (2024), 388-397 (DOI)
• A variation of the Mardesic Conjecture, Topology Proceedings 64 (2024), 103-120. (PDF)
• The Mardesic Conjecture for countably compact spaces, Topology and Its Applications 335 (2023), Paper No. 108596, 19 pp. (DOI)
• Archimedean positively ordered semigroups with maximal elements, Semigroup Forum 105 (2022), no. 1, 244-264. (Springer)
• Finite products of connected nowhere separable linearly ordered spaces, Topology and its Applications 300 (2021), Paper No. 107763, 21. (DOI)
• Continuous injections between the products of two connected nowhere real linearly ordered spaces, Topology Proc. 50 (2017), 319-333 (PDF)
• The comparison of various club guessing principles*, Annals of Pure and Applied Logic, 166 (2015), no. 5, 583-600. (DOI)
• The termination of the higher-dimensional tarai functions* (with M. Kikuchi), Information Processing Letters 115(2015) no. 2, 125-12. (DOI)
• $\mathbb{P}_{\rm{max}}$ variations for separating club guessing principles* (with P. Larson), Journal of Symbolic Logic 77 (2012), no. 2, 532-544. (DOI)
• Some results about $(+)$ proved by iterated forcing* (with P. Larson), Journal of Symbolic Logic 77 (2012), no. 2 515-531. (DOI)
• A sequel to a space topologized by functions from $\omega$ to $\omega$* (with A. Iwasa), Topology Proceedings, 38(2011), 309--312. (Top. Proc)
• Club guessing sequences - Natural structures in set theory -* (Japanese), Sugaku 62 (2) (2010), 453-478 (DOI) (English translation by myself in Sugaku Exposition 26 (2013), no. 1, 73-98)
• On Possible models of CH without locally compact sub-Ostaszewski spaces*, Topology Proceedings, 36(2010), 37-50. (Top. Proc.)
• Minimality of non $\sigma$-scattered orders (with Justin Moore), Fundamenta Mathematicae, 205 (2009), 29--44.
• A non-$D$-space with large extent*, Topology and Its Applications 155(11)(2008), 1256-1263. (DOI)
• A fine structure construction of a perfectly normal, non-realcompact space, Topology Proceedings 30(2) (2006), 533-545. (Topology Atlas)
• The saturation of club guessing ideals, Annals of Pure and Applied Logic 142(1-3)(2006), 398-424. (DOI)
• A tail club guessing ideal can be saturated without being a restriction of the non-stationary ideal, The Notre Dame Journal of Formal Logic, 46 (3)(2005), 327--333. (DOI)
• More on perfectly normal, non-realcompact spaces, Topology and Its Applications 153(9)(2006), 1476--1499. (DOI)
• $\alpha$-properness and Axiom A, Fundamenta Mathematicae, 186 (2005), 25--37.
• Club guessing sequences and filters, Journal of Symbolic Logic, 70 (4)(2005), 1037--1071. (DOI)
• A perfectly normal nonrealcompact space consistent with $\mathsf{MA}_{\aleph_{1}} (with Fernando Hernández-Hernández), Topology and Its Applications, 143 (1--3)(2004), 175--188. (DOI)
• Directive trees and games on posets (with Yasuo Yoshinobu), Proceedings of the American Mathematical Society, 130 (2002), 1477--1485. (AMS)

• Every cancellative topological semigroup on the finite product of connected linearly ordered topological spaces is separable, submitted (PDF)
• The invariance of domain theorem for the finite product of connected linearly ordered topological spaces, submitted (PDF)
• The precipitousness of tail club guessing ideals, submitted (PDF)

• Torsion elements of the autohomeomorphism group of R^2, submitted (PDF)

• The weak diamond, RIMS K{\^o}ky{\^u}roku, 2261 (2023), 43-46. (PDF)
• Qualitative differences between the real line and nonseparable linearly ordered topological spaces, RIMS K{\^o}ky{\^u}roku, 2198 (2021), 32-40. (PDF)

• IRP$\cap$LSI is not recursively enumerable. *(PDF)
• The weak diamond*(PDF) - the proof of "$2^{\aleph_0}<2^{\aleph_1}$ implies the weak diamond", (hopefully easier to read than the paper of Devlin and Shelah)
• Notes on higher-dimensional tarai functions* (with M. Kikuchi), preprint (arXiv, PDF)

• The Mardesic Conjecture for Countably Compact Spaces (PDF), The Canadian Mathematical Society Winter Meeting 2022, Scientific Session in Set theory and its applications, December 2022
• proof of the Mardesic Conjecture by using countable elementary submodels (PDF), Special Session in Set-Theoretic Topology, AMS Fall Southeastern Section Meeting, online, November 2021.
• A proof of Certanov's Theorem by using countable elementary submodels (PDF), Spring Topology and Dynamics Conference hosted by Murray State University, online, May 2021.
• Some results on the products of connected linearly ordered sets (PDF), Special Session in Set-Theoretic Topology, AMS Fall Southeastern Sectional Meeting at the University of North Carolina, Greensboro, November 2014.
• Injective continuous functions between the products of two connected nowhere real linearly ordered sets (PDF), Special Session in Set-Theoretic Topology, Spring Topology and Dynamics Conference at the University of Richmond, March 2014.
• A precipitous club guessing ideal on omega_1* (ESI workshop), ESI workshop on large cardinals and descriptive set theory, June, 2009
• The principle $(+)$ and club guessing sequences* (PDF), Boise Extravaganza in Set Theory at Boise State University, March 2008
• The comparison of various club guessing principles* (PDF), BLAST at University of Denver, August 2008

The above entries marked with a * are subject to the following acknowledgment and disclaimer:
This material is based upon work supported by the National Science Foundation under Grant No.~0700983.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.