Tychonoff theorem

Tychonoff theorem

[tī′kä‚nȯf ‚thir·əm]
(mathematics)
A product of topological spaces is compact if and only if each individual space is compact.
References in periodicals archive ?
In particular, we have proved the counterparts of Alexander's subbase lemma and Tychonoff theorem for fuzzy soft topological spaces.
Now we prove the counterparts of the well known Alexander's subbase lemma and the Tychonoff theorem for fuzzy soft topological spaces, the proofs of which are based on the proofs of the corresponding results given in [18] and [28], respectively.
In particular the counterparts of Alexander's subbase lemma and the Tychonoff theorem for fuzzy soft topological spaces have been proved.
The first seven chapters cover the usual topics of point-set or general topology, including topological spaces, new spaces from old ones, connectedness, the separation and countability axioms, and metrizability and paracompactness, as well as special topics such as contraction mapping in metric spaces, normed linear spaces, the Frechet derivative, manifolds, fractals, compactifications, the Alexander subbase, and the Tychonoff theorems. The final chapters were written to provide an introduction and motivation for the study of algebraic topology, with an emphasis on geometric applications.