Office: Pearce 201C
Email: gilsdlte @ cmich . edu
Research summary: I spend about half of my research time studying topological vector spaces, mainly locally convex spaces, and the other half studying cultural mathematics (also called ethnomathematics).
Book: Thomas E. Gilsdorf; Introduction
to Cultural Mathematics, with Case Studies in the Otomies
and Incas. Hoboken, NJ: John Wiley &
Sons, ©2012. This is the first book written specifically as a textbook for a
course on cultural mathematics or ethnomathematics. It can also be used as
secondary reference for courses in disciplines such as anthropology, history,
or mathematics education. In addition, the book can be used as a reference in
research projects. For a quick summary of the book, please see the Product
Flyer.
• Thomas E. Gilsdorf. Valdivia’s lifting theorem for non-metrizable spaces. Published in: Topology and its Applications, vol. 317, (2022), Paper No. 108160. Preprint: https://arxiv.org/abs/2205.15497 Journal access: https://www.sciencedirect.com/journal/topology-and-its-applications.
• Thomas E. Gilsdorf. Inductive limits of quasi locally Baire spaces. Published in: Asian-European Journal of Mathematics, vol. 15, no. 4, (2022), Paper No. 2250074. Preprint: https://arxiv.org/abs/2105.06358 . Journal website: https://www.worldscientific.com/worldscinet/aejm .
• Carlos Bosch, César L. García, Thomas E. Gilsdorf, Claudia Gómez-Wulschner, and Rigoberto Vera. Eventually constant intertwining linear maps between complete locally convex spaces. Published in: Italian Journal of Mathematics, 46, (2021), 147 - 163. Preprint: https://arxiv.org/abs/2003.14164 . Journal Access: https://ijpam.uniud.it/journal/onl_2021-46.htm .
• Carlos Bosch, César L. García, Thomas E. Gilsdorf, Claudia Gómez-Wulschner, and Rigoberto Vera. Fixed points of set-valued maps in locally complete spaces. Published in: Fixed Point Theory & Applications. Paper No. 13, 11, (2017).
• Carlos Bosch, César L. García, Thomas E. Gilsdorf, Claudia Gómez-Wulschner, and Rigoberto Vera. On Docile Spaces, Mackey First Countable Spaces, and Sequentially Mackey First Countable Spaces. International Journal of Mathematical Analysis, vol. 11, no. 8, (2017), 377 - 388. doi: 10.12988/ijma.2017.7234 Preprint: Arxiv.org/pdf/2003.14165.pdf.
• Thomas E. Gilsdorf and Mohammad Khavanin. Existence and uniqueness for nonlinear integro-differential equations in real locally complete spaces. Published in: Scientiae Mathematicae Japonicae, 76 (3): (2013), 395–400. Preprint: Arxiv.org/pdf/2003.09480.pdf.
• Carlos Bosch Giral, Thomas E. Gilsdorf, and
Claudia Gómez-Wulschner. Mackey
first countability and docile locally convex spaces. Published in: Acta Mathematica Sinica
(English Series), vol. 27 no. 4, (2011), 737–740.
• Thomas E. Gilsdorf. Locally convex theorems and some results of George Mackey (1916–2006). Published in: Miscelánea Matemática, 47, (2008), 39 - 53.
• Thomas E. Gilsdorf. Strictly webbed convenient locally convex spaces. Published in: International Journal of Mathematical Analysis, vol. 1, no. 13-16, (2007), 775–782.
• C. Bosch, A. Garcia, and T. Gilsdorf. Some hereditary properties of $l_\infty(E)$ from $E$. Published in: Int. Math. J., 2, no.11, (2002), 1061–1066.
• C. Bosch, T. Gilsdorf, C. Gómez, and R. Vera. Local completeness of $l_p(E)$, $1 \le p < \infty$. Int. J. Math. Math. Sci., 31(11):651–657, 2002.
• José N. Aguayo and Thomas E. Gilsdorf. Non-Archimedean vector measures and integral operators. In $p$-adic functional analysis (Ioannina, 2000), vol 222 Lecture Notes in Pure and Appl. Math., Dekker, New York, (2001), 1–11.
• Jerzy Kąkol, Thomas Gilsdorf, and Luis Sánchez Ruiz. Baire-likeness of spaces $l_\infty(E)$ and $c_0(E)$. Period. Math. Hungar., 40, no. 1 (2000), 31–35.
• Jerzy Kąkol and Thomas Gilsdorf. On the weak basis theorems for $p$-adic locally convex spaces. In $p$-adic functional analysis (Poznań, 1998), volume 207 of Lecture Notes in Pure and Appl. Math., pages 149–165. Dekker, New York, 1999.
• Thomas E. Gilsdorf and Jerzy Kakol. On some non-Archimedean closed graph theorems. In p-adic functional analysis (Nijmegen, 1996), volume 192 of Lecture Notes in Pure and Appl. Math., pages 153–158. Dekker, New York, 1997.
• Carlos Bosch and Thomas E. Gilsdorf. Strictly barrelled disks in inductive limits of quasi-(LB)-spaces. Internat. J. Math. Math. Sci., 19(4):727–732, 1996.
• Thomas E. Gilsdorf. A note on locally complete spaces. Rev. Colombiana Mat., 29(2):113– 117, 1995.
• Józef Burzyk and Thomas E. Gilsdorf. Some remarks about Mackey convergence. Internat. J. Math. Math. Sci., 18(4):659–664, 1995.
• C. Bosch, T. E. Gilsdorf, and J. Kučera. Remarks on the uniform boundedness principle. In Topological vector spaces, algebras and related areas (Hamilton, ON, 1994), volume 316 of Pitman Res. Notes Math. Ser., pages 16–19. Longman Sci. Tech., Harlow, 1994.
• Thomas E. Gilsdorf. Boundedly compatible webs and strict Mackey convergence. Math. Nachr., 159:139–147, 1992.
• Thomas E. Gilsdorf. Regular inductive limits of $\mathcal{K}$-spaces. Collect. Math., 42, (1):45–49, 1991.
• Thomas E. Gilsdorf. Corrigendum: "Mackey convergence and quasi-sequentially webbed spaces". Internat. J. Math. Math. Sci., 14(3):610, 1991.
• Thomas E. Gilsdorf. Mackey convergence and quasi-sequentially webbed spaces. Internat. J. Math. Math. Sci., 14(1):17–26, 1991.
• Thomas E. Gilsdorf. Bounded sets in $\mathcal{L}(E,F)$. Internat. J. Math. Math. Sci., 12(3):447–450, 1989.
• C. Bosch, T. Gilsdorf, and J. Kučera. A necessary and sufficient condition for weakly bounded sets to be strongly bounded. An. Inst. Mat. Univ. Nac. Autónoma México, 28:1–5 (1989), 1988.
• Thomas E. Gilsdorf. The Mackey convergence condition for spaces with webs. Internat. J. Math. Math. Sci., 11(3), (1988), 473–483.
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• Shalini Verma,
Thomas E. Gilsdorf. Learning Mathematics through Traditional Games. In preparation.
• Thomas E. Gilsdorf. Género, matemáticas culturales,
y arte textil de los Mazahuas y Otomíes. (Gender, cultural mathematics, and textile
art of the Mazahua and Otomi). Submitted
for publication, (2021).
• Shalini Verma,
Thomas E. Gilsdorf. An
ethnomathematical exploration of Warli art and its
integration with teaching mathematics. Accepted for publication in: Journal of Mathematics and Culture, (2022).
• Thomas E. Gilsdorf. Hñähñu (Otomi) mathematics revisited. Published in: Journal of Mathematics and Culture, vol. 10, no. 2, (2016), 73 - 85.
• Thomas E. Gilsdorf.
Gender, culture, and
ethnomathematics. In Proceedings of the Eighth International Conference on
Mathematics Education and Society (MES-8), Swapna Mukhopadhyay, Brian
Greer, Eds., (2015), 531-542.
• Thomas E.Gilsdorf. Ethnomathematics of the Inkas. Published in: Encyclopedia of the History of Science, Technology and Medicine in Non-Western Cultures. Selin, Helaine (Ed.) 2 (2014): 1079.
• Thomas E. Gilsdorf.
Mathematics of the Hñähñu: the Otomies. Published in: Journal
of Mathematics and Culture, 4, no. 1, (2009), 84 - 105.
• Thomas E. Gilsdorf.
Ethnomathematics of the Otomies. (Etnomatemáticas de los Otomíes). Estudios
de Cultura Otopame. Institute of
Anthropology, National University of Mexico (UNAM), 6, (2008), 167-181.
• Thomas E. Gilsdorf. Inca mathematics. In Mathematics across cultures, volume 2 of Sci. Across Cult. Hist. Non-West. Sci., pages 189–203. Kluwer Acad. Publ., Dordrecht, 2000.