Alexander Doniphan Wallace (21 August 1905 Hampton, Virginia, USA – 16 October 1985 New Orleans, USA) was an American mathematician who introduced proximity spaces.
Wallace received from the University of Virginia B.A. in 1935, M.A. in 1936 and Ph.D. in 1940. He was an instructor at Princeton University in 1940–1941 and became an assistant professor in mathematics at the University of Pennsylvania in 1941 and remained there until 1947. He was a professor and chair of the mathematics department at Tulane University in 1947-1963. From 1963 until his retirement in 1973 he was a mathematics professor at the University of Florida.
His doctoral students include Chung Tao Yang.
Selected articles
"A theorem on acyclicity". Bull. Amer. Math. Soc. 67: 123–124. 1961. MR 0124886. doi:10.1090/s0002-9904-1961-10534-x.
"Remarks on affine semigroups". Bull. Amer. Math. Soc. 66: 110–112. 1960. MR 0110768. doi:10.1090/s0002-9904-1960-10419-3.
"Factoring a lattice". Proc. Amer. Math. Soc. 9: 250–252. 1958. MR 0094306. doi:10.1090/s0002-9939-1958-0094306-1.
with R. J. Koch: "Admissibility of semigroup structures on continua". Trans. Amer. Math. Soc. 88: 277–287. 1958. MR 0095223. doi:10.1090/s0002-9947-1958-0095223-8.
"The peripheral character of central elements of a lattice". Proc. Amer. Math. Soc. 8: 596–597. 1957. MR 0087882. doi:10.1090/s0002-9939-1957-0087882-5.
"The structure of topological semigroups". Bull. Amer. Math. Soc. 61: 95–112. 1955. MR 0067907. doi:10.1090/s0002-9904-1955-09895-1.
"The position of $C$-sets in semigroups". Proc. Amer. Math. Soc. 6: 639–642. 1955. MR 0071709. doi:10.1090/s0002-9939-1955-0071709-x.
"Struct ideals". Proc. Amer. Math. Soc. 6: 634–638. 1955. MR 0071756. doi:10.1090/s0002-9939-1955-0071756-8.
"Topological invariance of ideals in mobs". Proc. Amer. Math. Soc. 5: 866–868. 1954. MR 0066399. doi:10.1090/s0002-9939-1954-0066399-5.
"Partial order and indecomposability". Proc. Amer. Math. Soc. 5: 780–781. 1954. MR 0064391. doi:10.1090/s0002-9939-1954-0064391-8.
"Boolean rings and cohomology". Proc. Amer. Math. Soc. 4: 475. 1953. MR 0055668. doi:10.1090/s0002-9939-1953-0055668-x.
"Extensional invariance". Trans. Amer. Math. Soc. 70: 97–102. 1951. MR 0041421. doi:10.1090/s0002-9947-1951-0041421-2.
"Cyclic invariance under multi-valued maps". Bull. Amer. Math. Soc. 55: 820–824. 1949. MR 0033534. doi:10.1090/s0002-9904-1949-09299-6.
"Extension sets". Trans. Amer. Math. Soc. 59: 1–13. 1946. MR 0014809. doi:10.1090/s0002-9947-1946-0014809-1.
"Dimensional types". Bull. Amer. Math. Soc. 51: 679–681. 1945. MR 0013302. doi:10.1090/s0002-9904-1945-08416-x.
"A fixed-point theorem". Bull. Amer. Math. Soc. 51, Part 1: 413–416. 1945. MR 0012221. doi:10.1090/s0002-9904-1945-08367-0.
"The acyclic elements of a Peano space". Bull. Amer. Math. Soc. 47: 778–780. 1941. MR 0004757. doi:10.1090/s0002-9904-1941-07568-3.
"A fixed-point theorem for trees". Bull. Amer. Math. Soc. 47: 757–760. 1941. MR 0004758. doi:10.1090/s0002-9904-1941-07556-7.
"On non-boundary sets". Bull. Amer. Math. Soc. 45: 420–422. 1939. MR 1563997. doi:10.1090/s0002-9904-1939-06997-8.
with D. W. Hall: "Some invariants under monotone transformations". Bull. Amer. Math. Soc. 45: 294–295. 1939. MR 1563969. doi:10.1090/s0002-9904-1939-06964-4.
