Products of Steiner's quasi-proximity spaces
Proc. Amer. Math. Soc. 51 (1975), 225-230
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Abstract: E. F. Steiner introduced a quasi-proximity satisfying for some of . The purpose of this paper is to describe the Tychonoff product of topologies in terms of Steiner's quasi-proximities. Whenever is the Steiner quasi-proximity space, the product proximity on can be given, by using the concept of finite coverings, as the smallest proximity on which makes each projection -continuous.
A. Naimpally and B.
D. Warrack, Proximity spaces, Cambridge Tracts in Mathematics
and Mathematical Physics, No. 59, Cambridge University Press, London-New
York, 1970. MR
0278261 (43 #3992)
F. Steiner, The relation between quasi-proximities and topological
spaces, Math. Ann. 155 (1964), 194–195. MR 0163278
W. Stevenson, Product proximities, Fund. Math.
76 (1972), no. 2, 157–166. MR 0305361
- S. A. Naimpally and B. D. Warrack, Proximity spaces, Cambridge Tracts in Math. and Math. Phys., no. 59, Cambridge Univ. Press, London and New York, 1970. MR 43 #3992. MR 0278261 (43:3992)
- E. F. Steiner, The relation between quasi-proximities and topological spaces, Math. Ann. 155 (1964), 194-195. MR 29 #581. MR 0163278 (29:581)
- F. W. Stevenson, Product proximities, Fund. Math. 76 (1972), 157-166. MR 46 #4491. MR 0305361 (46:4491)
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