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Topologies generated by ideals

Carlos Uzcátegui (2006)

Commentationes Mathematicae Universitatis Carolinae

A topological space $X$ is said to be generated by an ideal $ℐ$ if for all $A \subseteq X$ and all $x \in \bar{A}$ there is $E \subseteq A$ in $ℐ$ such that $x \in \bar{E}$ , and is said to be weakly generated by $ℐ$ if whenever a subset $A$ of $X$ contains $\bar{E}$ for every $E \subseteq A$ with $E \in ℐ$ , then $A$ itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Hausdorff spaces). Another paradigmatic example is the class of Alexandroff spaces which corresponds to spaces generated by finite sets....

Topologies in atomic quantum logics

Zdena Riečanová (1989)

Acta Universitatis Carolinae. Mathematica et Physica

Topologies in product which preserve Baire spaces

Anna Kucia (1990)

Commentationes Mathematicae Universitatis Carolinae

Topologies of Chains.

R.A. ALO, O. FRINK (1967)

Mathematische Annalen

Topologies on free monoids induced by closure operators of a special type

Helmut Prodinger (1980)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Topologies on free monoids induced by families of languages

Helmut Prodinger (1983)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Topologies on generalized semi-inner product spaces

B. Nath (1971)

Compositio Mathematica

Topologies on groups determined by right cancellable ultrafilters

Igor V. Protasov (2009)

Commentationes Mathematicae Universitatis Carolinae

For every discrete group $G$ , the Stone-Čech compactification $β G$ of $G$ has a natural structure of a compact right topological semigroup. An ultrafilter $p \in G^{*}$ , where $G^{*} = β G ∖ G$ , is called right cancellable if, given any $q, r \in G^{*}$ , $q p = r p$ implies $q = r$ . For every right cancellable ultrafilter $p \in G^{*}$ , we denote by $G (p)$ the group $G$ endowed with the strongest left invariant topology in which $p$ converges to the identity of $G$ . For any countable group $G$ and any right cancellable ultrafilters $p, q \in G^{*}$ , we show that $G (p)$ is homeomorphic to $G (q)$ if and only if...