Displaying similar documents to “Some properties of maximal open sets.”

On weak type inequalities for rare maximal functions in ℝⁿ

A. M. Stokolos (2006)

Colloquium Mathematicae


The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.

Applications of maximal μ-open sets in generalized topology and quasi topology

Bishwambhar Roy, Ritu Sen (2013)

Discussiones Mathematicae - General Algebra and Applications


In this paper, some fundamental properties of maximal μ-open sets such as decomposition theorem for a maximal μ-open set, are given in a generalized topological space. Some basic properties of intersection of maximal μ-open sets are established, cohere the law of μ-radical μ-closure in a quasi topological space is obtained, among the other things.

Maximal pseudocompact spaces and the Preiss-Simon property

Ofelia Alas, Vladimir Tkachuk, Richard Wilson (2014)

Open Mathematics


We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y. It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant...

Maximal functions and related weight classes.

Carlo Sbordone, Ingemar Wik (1994)

Publicacions Matemàtiques


The famous result of Muckenhoupt on the connection between weights w in A-classes and the boundedness of the maximal operator in L(w) is extended to the case p = ∞ by the introduction of the geometrical maximal operator. Estimates of the norm of the maximal operators are given in terms of the A-constants. The equality of two differently defined A-constants is proved. Thereby an answer is given to a question posed by R. Johnson. For non-increasing functions on the positive real line a...