Results 31 to 40 of about 433 (82)
Compactness of powers of \omega
, 2013 We characterize exactly the compactness properties of the product of \kappa\ copies of the space \omega\ with the discrete topology. The characterization involves uniform ultrafilters, infinitary languages, and the existence of nonstandard elements in ...
Lipparini, Paolo
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Ultrafilter convergence in ordered topological spaces [PDF]
, 2014 We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness are equivalent.
Lipparini, Paolo
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International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 199-200, 1998., 1998 In this paper we give an embedding characterization of θ‐regularity using the Wallman‐type compactlfication. The productivity of θ‐regularity and a slight generalization of Nagami′s Product Theorem to non‐Hausdorff paracompact ∑‐spaces we obtain as a corollary.
Martin M. Kovár
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, 2019 Let $x$ be a sequence taking values in a separable metric space and $\mathcal{I}$ be a generalized density ideal or an $F_\sigma$-ideal on the positive integers (in particular, $\mathcal{I}$ can be any Erd{\H o}s--Ulam ideal or any summable ideal). It is
Balcerzak +31 more
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A note on some applications of semi‐open sets
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 205-207, 1998., 1996 The object of the present paper is to study the well known notions of semi‐closure, semiinterior, semi‐frontier and semi‐exterior of a set using the concept of semi‐open sets. A semi‐isolated point of a set is also defined and studied.
T. M. Nour
wiley +1 more source
On strong form of Arzela convergence
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 417-421, 1997., 1996 We define some new type of convergence of nets of functions which is formulated in terms of open covers. It preserves continuity and under some assumptions implies (or coincides with) the Arzela quasi‐uniform convergence. Furthermore, the introduced strong convergence is used for characterization of compactness and regularity of a topological space.
Janina Ewert
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Function spaces and contractive extensions in Approach Theory: The role of regularity
, 2013 Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to convergence-approach spaces ...
Colebunders, Eva +2 more
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Compactifying a convergence space with functions
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 657-666, 1996., 1995 A convergence space is a set together with a convergence structure. In this paper we discuss a method of constructing compactifications on a class of convergence spaces by use of functions.
Robert P. André
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Some more Problems about Orderings of Ultrafilters [PDF]
, 2010 We discuss the connection between various orders on the class of all the ultrafilters and certain compactness properties of abstract logics and of topological spaces. We present a model theoretical characterization of Comfort order.
Lipparini, Paolo
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One‐point compactification on convergence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 277-282, 1994., 1993 A convergence space is a set together with a notion of convergence of nets. It is well known how the one‐point compactification can be constructed on noncompact, locally compact topological spaces. In this paper, we discuss the construction of the one‐point compactification on noncompact convergence spaces and some of the properties of the one‐point ...
Shing S. So
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