In this paper, a simple proof is given for the following theorem due to Blair [7], Blair-Hager [8] and Hager-Johnson [12]: A Tychonoff space X is z-embedded in every larger Tychonoff space if and only if X is almost compact or Lindelöf. We also give a simple proof of a recent theorem of Bella-Yaschenko [6] on absolute embeddings.

The purpose of this paper is to prove a Tychonoff theorem in the so-called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some ...

The Tychonoff Theorem is discussed with respect to point-free topology, from the point of view of both topos-valid and predicative mathematics. A new proof is given of the infinitary Tychonoff Theorem using predicative, choice-free methods for possibly undecidable index set. It yields a complete description of the finite basic covers of the product.

In this paper, we prove the following statements: (1) There exist a Tychonoff space X and a subspace Y of X such that Y is strongly star-Lindelöf in X and e(Y, X) is arbitrarily large, but X is not star-Lindelöf. (2) There exist a Tychonoff space X and a subspace Y of X such that Y is star-Lindelöf in X, but Y is not strongly star-Lindelöf in X.

This paper presents a new consistent example of a relatively normal subspace which is not Tychonoff.

A sharp base B is a base such that whenever (Bi)i<ω is an injective sequence from B with x ∈ i<ω Bi, then { ⋂ i<n Bi : n < ω} is a base at x. Alleche, Arhangel’skĭı and Calbrix asked: if X has a sharp base, must X × [0, 1] have a sharp base? Good, Knight and Mohamad claimed to construct an example of a Tychonoff space P with a sharp base such that P × [0, 1] does not have a sharp base. However,...

We consider when one-to-one continuous mappings can improve normalitytype and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space X there is a μ such that X can be condensed onto a normal (σ-compact) space if and only if there is no measurable cardinal. For any Tychonoff space X and any cardinal ν there is a Tychonoff space M which preserv...