https://www.math.tugraz.at/~ganster/papers/74.pdf

On generalized closed sets

In this paper, we continue the study of generalized closed sets in a topological space. In particular, we study the question when some classes of generalized closed sets coincide. A new class of spaces, the class of sg-submaximal spaces, is also introduced. Characterizations of extremally disconnected spaces and sg-submaximal spaces are established via various kinds of generalized closed sets. 1. I~vTR~DUCTI~N During the last few years the study of generalized closed sets has found consid- erable interest among general topologists. One reason is these objects are natural generalizations of closed sets. More importantly, generalized closed sets suggest some new separation axioms which have been found to be very useful in the study of certain objects of digital topology, for example, the digital line (see e.g. (S)). In (5), Dontchev summarized in a diagram the fundamental relationships between the various types of generalized closed sets. Concerning this diagram, he also posed two questions which have been answered by Cao, Ganster and Reilly in (4). In the present paper, we take another look at Dontchev's diagram. In doing so, we are able to characterize extremally disconnected spaces via generalized closed sets. Moreover, we introduce the notion of sg-submaximal spaces and investigate this class of spaces in terms of the Hewitt decomposition of a topological space.

/pdf/submaximality-extremal-disconnectedness-and-generalized-2n2lxqzmj4.pdf

Submaximality, extremal disconnectedness and generalized closed sets

The aim of this paper is to continue the study of sg-compact spaces, a topological notion much stronger than hereditary compactness We investigate the rela- tions between sg-compact and C2-spaces and the interrelations to hereditarily sg-closed sets

/pdf/more-on-sg-compact-spaces-50zl8ebkvd.pdf

More on sg-compact spaces *

This paper continues the study of preclosed sets and of generalized preclosed sets in a topological space Our main objective is to establish results about the relationships between the various types of generalized closed sets As a by product we are able to provide characterizations of certain known classes of topological spaces by using preclosed sets and their generalizations

/pdf/on-preclosed-sets-and-their-generalizations-1521ovcjau.pdf

On preclosed sets and their generalizations

We introduce a new class of functions called weakly b-continuous which is included in the class of weakly β -continuous functions due to Popa and Noiri [Popa V, Noiri T. Weakly β -continuous functions. An Univ Timis Ser Mat-Inform 1994;32(2):83–92]. Some characterizations and several properties concerning weak b-continuity are obtained. Furthermore relationships among strong θ -b-continuity, b-continuity, weak b-continuity and faint b-continuity are investigated.

R. Devi

Papers

Remarks on Semi-generalized Closed Sets and Generalized Semi-closed Sets