Some characterizations of -dimensional -spaces

Author:
M. J. Canfell

Journal:
Trans. Amer. Math. Soc. **159** (1971), 329-334

MSC:
Primary 54.70; Secondary 46.00

MathSciNet review:
0279784

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we obtain characterizations of an -dimensional -space in terms of the rings of continuous real-valued and complex-valued functions defined on the space. Motivation for these results is the work of Gillman and Henriksen on -spaces (-spaces of dimension 0) and -spaces (-spaces of dimension 0 or 1).

**[1]**F. F. Bonsall and B. J. Tomiuk,*The semi-algebra generated by a compact linear operator*, Proc. Edinburgh Math. Soc. (2)**14**(1964/1965), 177–196. MR**0184083****[2]**M. J. Canfell,*Uniqueness of generators of principal ideals in rings of continuous functions*, Proc. Amer. Math. Soc.**26**(1970), 571–573. MR**0288109**, 10.1090/S0002-9939-1970-0288109-8**[3]**J. R. Gard and R. D. Johnson,*Four dimension equivalences*, Canad. J. Math.**20**(1968), 48–50. MR**0222863****[4]**Leonard Gillman and Melvin Henriksen,*Some remarks about elementary divisor rings*, Trans. Amer. Math. Soc.**82**(1956), 362–365. MR**0078979**, 10.1090/S0002-9947-1956-0078979-8**[5]**Leonard Gillman and Melvin Henriksen,*Rings of continuous functions in which every finitely generated ideal is principal*, Trans. Amer. Math. Soc.**82**(1956), 366–391. MR**0078980**, 10.1090/S0002-9947-1956-0078980-4**[6]**Leonard Gillman and Meyer Jerison,*Rings of continuous functions*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0116199****[7]**Meyer Jerison,*Rings of germs of continuous functions*, Functional Analysis (Proc. Conf., Irvine, Calif., 1966) Academic Press, London; Thompson Book Co., Washington, D.C., 1967, pp. 168–174. MR**0221290****[8]**Max L. Weiss,*Some separation properties in sup-norm algebras of continuous functions*, Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965) Scott-Foresman, Chicago, Ill., 1966, pp. 93–97. MR**0193536**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
54.70,
46.00

Retrieve articles in all journals with MSC: 54.70, 46.00

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0279784-8

Keywords:
-dimensional,
-space,
Hermite ring,
-ring,
rings of continuous functions

Article copyright:
© Copyright 1971
American Mathematical Society