Beshimov, R. B. Safarova, D. T.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper, the connection between a finally compact, pceudocompact, extremely disconnected, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\aleph$$\end{doc...

Bhattacharjee, Papiya Knox, Michelle L. McGovern, Warren Wm.

It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space can ever be extremally disconnected. We answer this question in the affirmative; an example of va...

Lekše, Maruša

Ekstremno nepovezani prostori so prostori, v katerih je zaprtje vsake odprte množice odprta množica. V tem diplomskem delu se osredotočimo na nekatere zanimive lastnosti ekstremno nepovezanih prostorov Tihonova. Pokažemo, da je v takšnih prostorih vsako konvergentno zaporedje od nekega člena naprej konstantno. Doka- žemo, da je prostor Tihonova eks...

Osipov, A. V. Pytkeev, E. G.
Published in
Proceedings of the Steklov Institute of Mathematics

For a Tychonoff space X, we obtain a criterion of the σ-countable compactness of the space of continuous functions C(X) with the set-open topology. In particular, for the class of extremally disconnected spaces X, we prove that the space Cλ(X) is σ-countably compact if and only if X is a pseudocompact space, the set X(P) of all P-points of the spac...

McGovern, Warren Wm.
Published in
Acta Mathematica Hungarica

We study two rings of quotients of C(X), the ring of continuous functions on the Tychonoff space X. The first, F(X), is the ring of quotients induced by the filter of ideals consisting of dense finite intersections of fixed maximal ideals. The second, C[F], is the ring of quotients induced by the filter of dense cofinite subspaces of X. After some ...

Drozdovskii, S. A. Filippov, V. V.
Published in
Mathematical Notes

A new class of set-valued maps that includes all upper and lower semicontinuous set-valued maps is introduced. For this class, a selection theorem having applications in the theory of differential inclusions is presented.