The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω < λ κ , no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a s...

Propounding a general categorical framework for the extension of dualities, we present new proof de Vries Duality Theorem category KHaus compact Hausdorff spaces and their continuous maps, as an restricted Stone duality. Then, applying dualization to duality, give alternative duality Tych Tychonoff that was provided by Bezhanishvili, Morandi Olberding. In process doing so, obtain theorems both ...

Abstract We introduced the fuzzy axioms of choice, Zorn’s lemma and well-ordering principle, which are versions discussed relations among them. As an application lemma, we got following results: (1) Every proper ideal a ring was contained in maximal ideal. (2) nonzero (3) Introduced notion nilpotent elements R , proved that intersection all prime ideals commutative is union . (4) Proposed versi...

‎let ${x_{alpha}:alphainlambda}$ be a collection of topological spaces‎, ‎and $mathcal {g}_{alpha}$ be a grill on $x_{alpha}$ for each $alphainlambda$‎. ‎we consider tychonoffrq{}s type theorem for $x=prod_{alphainlambda}x_{alpha}$ via the above grills and a natural grill on $x$ ‎related to these grills, and present a simple proof to this theorem‎. ‎this immediately yields the classical theorem...

We say that a Tychonoff space X has computable z-radicals if for all ideals a of C(X), the smallest z-ideal containing a is generated as an ideal by all the s◦f , where f is in a and s is a continuous function IR −→ IR with s−1(0) = {0}. We show that every cozero set of a compact space has computable z-radicals and that a subset X of IR has computable z-radicals if and only if X is locally closed.

The aim of this paper is to introduce a new notion of L-fuzzy compactness in L-fuzzy topological spaces, which is a generalization of Lowen’s fuzzy compactness in L-topological spaces. The union of two L-fuzzy compact L-sets is L-fuzzy compact. The intersection of an L-fuzzy compact L-set G and an L-set H with T(H) = ⊤ is L-fuzzy compact. The L-fuzzy continuous image of an L-fuzzy compact L-set...

A Tychonoff space X such that the maximum ring of quotients of C(X) is uniformly complete is called a uniform quotients space. It is shown that this condition is equivalent to the Dedekind– MacNeille completion of C(X) being a ring of quotients of C(X), in the sense of Utumi. A compact metric space is a uniform quotients space precisely when it has a dense set of isolated points. Extremally dis...

We say that a Tychonoff space X has computable z-radicals if for all ideals a of C(X), the smallest z-ideal containing a is generated as an ideal by all the s ◦ f , where f is in a and s is a continuous function IR −→ IR with s−1(0) = {0}. We show that every cozero set of a compact space has computable z-radicals and that a subset X of IR has computable z-radicals if and only if X is locally cl...