a subgroup $x$ of a group $g$ is almost normal if the index $|g:n_g(x)|$ is finite, while $x$ is nearly normal if it has finite index in the normal closure $x^g$. this paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.

We explore almost-normality in Isbell-Mr\'owka spaces and some related concepts. use forcing to provide an example of almost-normal not normal almost disjoint family, the concept semi-normality spaces, define strongly $(\aleph_0, <\mathfrak c)$-separated families prove generic existence completely separable c)$-almost assuming $\mathfrak s=\mathfrak c$ b=\mathfrak c$. also a Tychonoff pseudocom...

In this paper by using rgα−open sets I define almost rgα−normality and mild rgα−normality also we continue the study of further properties of rgα−normality. We show that these three axioms are regular open hereditary. I also define the class of almost rgα−irresolute mappings and show that rgα−normality is invariant under almost rgα−irresolute M-rgα−open continuous surjection.

In this paper we define almost rg-normality and mild rg-normality, continue the study of further properties of rgnormality. We show that these three axioms are regular open hereditary. Also define the class of almost rg-irresolute mappings and show that rg-normality is invariant under almost rg-irresolute M-rg-open continuous surjection. AMS Subject Classification: 54D15, 54D10.

We introduce a new class of functions called almost gs-closed and use the functions to improve several preservation theorems of normality and regularity and also their generalizations. The main result of the paper is that normality and weak normality are preserved under almost gs-closed continuous surjections.

In the previous chapter we considered estimator of several different parameters. The hope is that as the sample size increases the estimator should get ‘closer’ to the parameter of interest. When we say closer we mean to converge. In the classical sense the sequence {xk} converges to x (xk → x), if |xk − x| → 0 as k → ∞ (or for every ε > 0, there exists an n where for all k > n, |xk − x| < ε). ...