MATHEMATICS

On some Equivalences on the Class of Tychonoff Spaces

V. R. Lazarev

Tomsk State University, Faculty of Mechanics and Mathematics

Abstract: Some method, generating the equivalence relations between Tychonoff spaces, is presented. It is shown, that $l$-, $u$-, and $t$-equivalences are particular cases of this general construction. The new examples of equivalences, preserving compactness, Lindelöf number and dimension, are given.

Keywords: the space of continuous functions, $l$-equivalence, $t$-equivalence.

UDC: 515.12


Accepted: October 16, 2008