Parabolic Green Functions in Open Sets

On Pre-θ-Open Sets and Two Classes of Functions

on pre-θ-open sets and two classes of functions

Nonlinear Parabolic Capacity and Polar Sets of Superparabolic Functions

We extend the theory of the thermal capacity for the heat equation to nonlinear parabolic equations of the p-Laplacian type. We study definitions and properties of the nonlinear parabolic capacity and show that the capacity of a compact set can be represented via a capacitary potential. As an application, we show that polar sets of superparabolic functions are of zero capacity. The main technic...

$r$-fuzzy regular semi open sets in smooth topological spaces

In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...

Some results on maximal open sets

In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.