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Full-Text Articles in Applied Mathematics
Entropy In Topological Groups, Part 2, Dikran Dikranjan
Entropy In Topological Groups, Part 2, Dikran Dikranjan
Summer Conference on Topology and Its Applications
Entropy was introduced first in thermodynamics and statistical mechanics, as well as information theory. In the last sixty years entropy made its way also in topology, ergodic theory, as well as other branches of mathematics as algebra, geometry and number theory where dynamical systems appear in one way or another.
Roughly speaking, entropy is a non-negative real number or infinity assigned to a "selfmap" T of a "space" X, where the "space" X can be a topological or uniform space, a measure space, an abstract or topological group (or vector space) or just a set. The "selfmap" T can be, …
On Cardinality Bounds Involving The Weak Lindelöf Degree And H-Closed Spaces, Nathan Carlson, Angelo Bella, Jack Porter
On Cardinality Bounds Involving The Weak Lindelöf Degree And H-Closed Spaces, Nathan Carlson, Angelo Bella, Jack Porter
Summer Conference on Topology and Its Applications
1. Bella and Carlson give several classes of spaces X for which |X| ≤ 2wL(X)χ(X). This includes locally compact spaces and, more recently, extremally disconnected spaces. Three proofs of the former lead to more general results. One such result is that any regular space X with a π-base consisting of elements with compact closure satisfies |X| ≤ 2wL(X)χ(X). It is also shown that if X is locally compact and power homogeneous that |X| ≤ 2wL(X)t(X), an extension of De la Vega's Theorem.
2. Porter and Carlson give a new cardinality bound for any Hausdorff …