An answer to a question of Pyrih

We answer a recent question of Pyrih by proving that a topological space $(X,\tau)$ is open-normal if and only if it is extremally disconnected.Comment: 2 pages, to appear in "Questions and Answrs in General Topology

Survey on preopen sets

The aim of this survey article is to cover most of the recent research on preopen sets. I try to present majority of the results on preopen sets that I am aware of.Comment: To appear in the Proceedings of the 1998 Yatsushiro Topological Conference, 22-23 August 199

Idealization of Ganster-Reilly decomposition theorems

In 1990, Ganster and Reilly proved that a function is continuous if and only if it is precontinuous and LC-continuous. In this paper we extend their decomposition of continuity in terms of ideals. We show that a function $f \colon (X,\tau,{\cal I}) \to (Y,\sigma)$ is continuous if and only if it is pre-I-continuous and I-LC-continuous. We also provide a decomposition of I-continuity.Comment: 11 page

An Inverse Function Theorem for Metrically Regular Mappings

We prove that if a mapping F:X to Y, where X and Y are Banach spaces, is metrically regular at x for y and its inverse F^{-1} is convex and closed valued locally around (x,y), then for any function G:X to Y with lip G(x)regF(x|y)) < 1, the mapping (F+G)^{-1} has a continuous local selection around (x, y+G(x)) which is also calm

On a stronger form of hereditary compactness in product spaces

The aim of this paper is to continue the study of sg-compact spaces. The class of sg-compact spaces is a proper subclass of the class of hereditarily compact spaces. In our paper we shall consider sg-compactness in product spaces. Our main result says that if a product space is sg-compact, then either all factor spaces are finite, or exactly one factor space is infinite and sg-compact and the remaining ones are finite and locally indiscrete.Comment: 9 page

An answer to a question of Coleman on scattered sets

The aim of this paper is to show that every scattered subset of a dense-in-itself semi-$T_D$-space is nowhere dense. We are thus able to answer a recent question of Coleman in the affirmative. In terms of Digital Topology, we prove that in semi-$T_D$-spaces with no open screen, trace spaces have no consolidations.Comment: 5 page

A note on Saleh's paper `Almost continuity implies closure continuity'

Recently, Saleh claimed to have solved `a long standing open question' in Topology; namely, he proved that every almost continuous function is closure continuous (= $\theta$-continuous). Unfortunately, this problem was settled long time ago and even a better result is known.Comment: 2 pages, to appear in "Glasgow Math. J.

More on sg-compact spaces

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 relations between sg-compact and $C_2$-spaces and the interrelations to hereditarily sg-closed sets.Comment: 8 page

Contra-semicontinuous Functions

The aim of this paper is to introduce and study the concept of a contra-semicontinuous function and further investigate the class of strongly $S$-closed spaces. We obtain some new decompositions of generalized continuous functions.Comment: 12 page

A remark on β\beta-locally closed sets

The aim of this note is to show that every subset of a given topological space is the intersection of a preopen and a preclosed set, therefore $\beta$-locally closed, and that every topological space is $\beta$-submaximal.Comment: Mem. Fac. Sci. Kochi Univ. Ser. A Math., 20 (1999), to appea