# People

## Richard Sher

### Professor Emeritus

**Starting year at UNCG:** 1974**Ending year at UNCG:** 1996

### Education

**Degree(s): **Ph.D. in Mathematics, University of Utah (1966)

### Selected Publications

- with I. Ivanšić and J. E. Keesling “Introduction [in recognition of the achievements of Sibe Mardešić,” Geometric topology: Dubrovnik 1998. Topology Appl. 113 (2001), no. 1-3, 1-5.
- with B. Fitzpatrick, “B. J. Ball: An appreciation.” Special issue in memory of B. J. Ball, Topology Appl. 94 (1999), no. 1-3, 3-6.
- with A. Koyama, “Approximable dimension and acyclic resolutions,” Fund. Math. 152 (1997), no. 1, 43–53.
- with A. Chigogidze, and K. Kawamura, K., “Finiteness results in $$n$$-homotopy theory,” Proceedings of the International Conference on Set-theoretic Topology and its Applications (Matsuyama, 1994). Topology Appl. 74 (1996), no. 1-3, 3–16.
- “A wild $$k$$-dimensional Menger compactum in $$R^{2k+1}$$ all cell-like subsets of which are cellular. Continua (Cincinnati, OH, 1994), 343–345, Lecture Notes in Pure and Appl. Math., 170, Dekker, New York, 1995.
- “Max Dehn and Black Mountain College,” Math. Intelligencer 16 (1994), no. 1, 54–55.
- “A complement theorem in the universal Menger compactum,” Proc. Amer. Math. Soc. 121 (1994), no. 2, 611–618.
- with T. B. Rushing, “A cellular wedge in $$R^3$$,” Proc. Amer. Math. Soc. 113 (1991), no. 3, 895–898
- “On the separation of the plane by the closed one-to-one image of the reals,” Proceedings of the Guilford College Sesquicentennial Topology Conference, 1988 (Greensboro, NC, 1988), 29, Guilford College, Greensboro, NC, 1988.
- “Some examples concerning relative fundamental dimension and fundamental skeletal.” Proceedings of the Guilford College Sesquicentennial Topology Conference, 1988 (Greensboro, NC, 1988), 27–28, Guilford College, Greensboro, NC, 1988.
- with G. A. Venema, “Finite-dimensional complement theorems: examples and results, “Proc. Amer. Math. Soc. 103 (1988), no. 1, 299–306.
- “Complement theorems in shape theory. II,” Geometric topology and shape theory (Dubrovnik, 1986), 212–220, Lecture Notes in Math., 1283, Springer, Berlin, 1987.
- “A complement theorem for shape concordant compacta,” Proc. Amer. Math. Soc. 91 (1984), no. 1, 123-132.
- “Complement theorems in shape theory,” Shape theory and geometric topology (Dubrovnik, 1981), pp. 150–168, Lecture Notes in Math., 870, Springer, Berlin-New York, 1981.
- with I. Ivanšić, and G. A. Venema, “Complement theorems beyond the trivial range,” Illinois J. Math. 25 (1981), no. 2, 209-220.
- “Some alternative notions of position,” Proceedings of the International Conference on Geometric Topology (Warsaw, 1978), pp. 399–407, PWN, Warsaw, 1980.
- with I. Ivanšić, “A complement theorem for continua in a manifold,” The Proceedings of the 1979 Topology Conference (Ohio Univ., Athens, Ohio, 1979). Topology Proc. 4 (1979), no. 2, 437–452 (1980).
- with John G. Hollingsworth, “Closed manifolds are of simple shape,” Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 3, 287–290.
- with Laurence Boxer, “Borsuk’s fundamental metric and shape domination,” Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 9-10, 849-853.
- “Liftings of shape morphisms to finite covers,” Proceedings of the 1978 Topology Conference (Univ. Oklahoma, Norman, Okla., 1978), I. Topology Proc. 3 (1978), no. 1, 205–220 (1979).
- “Products and sums of absolute proper retracts,” II. Colloq. Math. 40 (1978/79), no. 2, 223-225.
- with James Keesling, “Shape properties of the Stone-_ech compactification,” General Topology and Appl. 9 (1978), no. 1, 1–8.
- with J. G. Hollingsworth, “On the cancellation of shapes from products,” Proceedings of the 1977 Topology Conference (Louisiana State Univ., Baton Rouge, La., 1977), II. Topology Proc. 2 (1977), no. 2, 479–482 (1978).
- “The union of two Hilbert cubes meeting in a Hilbert cube need not be a Hilbert cube,” Proc. Amer. Math. Soc. 63 (1977), no. 1, 150–152.
- “Extensions, retracts, and absolute neighborhood retracts in proper shape theory,” Fund. Math. 96 (1977), no. 2, 149–159.
- “Shape-docility at infinity and shape retraction,” Houston J. Math. 3 (1977), no. 1, 113–124. (Reviewer: Ju. M. Smirnov)
- “A survey of some results in geometric topology, J. Elisha Mitchell Sci. Soc. 92 (1976), no. 3, 98–103.
- “The cardinality of positions of simple closed curves in $$E^{3}$$ is $$2^{aleph _{0}}$$. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), no. 11, 1007–1010.
- “Docility at infinity and compactifications of ANR’s,” Trans. Amer. Math. Soc. 221 (1976), no. 1, 213–224.
- “Products and sums of absolute proper retracts,” Colloq. Math. 33 (1975), no. 1, 91–102.
- “Proper shape theory and neighborhoods of sets in $$Q$$-manifolds,” Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 23 (1975), no. 3, 271-276.
- “A theory of absolute proper retracts. Fund. Math. 88 (1975), no. 3, 241–247.
- with B. J. Ball, “A theory of proper shape for locally compact metric spaces,” Fund. Math. 86 (1974), 163–192.
- “Property $$SUV^{infty }$$ and proper shape theory,” Trans. Amer. Math. Soc. 190 (1974), 345-356.
- with B .J. Ball, “A theory of proper shape for locally compact metric spaces,” Bull. Amer. Math. Soc. 79 (1973), 1023–1026.
- with B. J. Ball, “Extending cell-like maps on manifolds,” Trans. Amer. Math. Soc. 186 (1973), 229–246 (1974).
- with B. J. Ball, “Embedding circle-like continua in $$E^{3}$$,” Canad. J. Math. 25 (1973), 791-805.
- “Realizing cell-like maps in Euclidean space,” General Topology and Appl. 2 (1972), 75–89.
- with John Hollingsworth, Triangulating neighborhoods in topological manifolds. General Topology and Appl. 1 (1971), 345–348.
- “Tame polyhedra in wild cells and spheres,” Proc. Amer. Math. Soc. 30 1971 169–174.
- “Determining the cellularity of a $$i$$-complex by properties of its arcs,” Proc. Amer. Math. Soc. 26 1970 491–498.
- “A result on unions of flat cells,” Duke Math. J. 37 1970 85–88.
- “Geometric embedding invariants of simple closed curves in three-space,” Duke Math. J. 36 1969 683–693.
- “Defining subsets of manifolds by cells,” Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 17 1969 363-365.
- with W. R Alford, “Defining sequences for compact 0

0-dimensional decompositions of En En

,” Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 17 1969 209–212.

- “Families of arcs in $$E^{3}$$,” Trans. Amer. Math. Soc. 143 1969 109–116.
- “Concerning wild Cantor sets in $$E^{3}$$,” Proc. Amer. Math. Soc. 19 1968 1195–1200.
- “Defining subsets of $$E^{3}$$ by cubes,” Pacific J. Math. 25 1968 613–619.
- with W. R. Alford, “A note on $$0$$-dimensional decompositions of $$E^{n}$$,” Amer. Math. Monthly 75 1968 377-378.
- “A note on an example of Stallings,” Proc. Amer. Math. Soc. 19 1968 619–620.
- with H. W. Lambert, “Point-like$$0$$-dimensional decompositions of $$S^{3}$$”, Pacific J. Math. 24 1968 511–518.
- “Toroidal decompositions of $$E^{3}$$,” Fund. Math. 61 1967/1968 225–241.

### Book:

Handbook of Geometric Topology,(Edited with R. J. Daverman), Elsevier, 2002.

### Brief Biography

Dick Sher came to UNCG in 1974. He was head of the department from 1981-1986, and he retired in 1996. Dick received a B.S. degree from The Michigan College of Mining and Technology (now Michigan Technological University) in 1960. After one year of graduate work at the University of Utah, he served for two years in the United States Army. Returning to the University of Utah, he received the M.S. in mathematics in 1964 and the Ph.D. in mathematics in 1966. His Ph.D. advisor was the noted topologist C. E. Burgess. The title of his dissertation: “Toroidal decompositions of E^{3}.” After graduation from the University of Utah, Dick joined the faculty at the University of Georgia (1966-1974). In addition to his time at Georgia and UNCG, he was a member of the Institute for Advanced Study during the academic year 1969-70 and the fall semester of 1986.

Dick Sher and Jerry Vaughan were Editors-in-Chief of the international research journal “Topology and its Applications,” from 1979-2000. “Topology and its Applications” is devoted to research in many areas of topology, and is published by Elsevier Science B.V. in Amsterdam. After Sher retired from the university he became a member of the Advisory Board of the journal from 2000-2007.

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