scholarly journals The lattice of topologies: A survey equations

1975 ◽  
Vol 5 (2) ◽  
pp. 177-198 ◽  
Author(s):  
Roland E. Larson ◽  
Susan J. Andima
Keyword(s):  
Lattice Of Topologies

The Meet Operator in the Lattice of Group Topologies

1986 ◽  
Vol 29 (4) ◽  
pp. 478-481
Author(s):  
Bradd Clark ◽  
Victor Schneider
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Locally Compact Group ◽  
Group Topology ◽  
Locally Compact ◽  
Hausdorff Topology ◽  
Lattice Of Topologies ◽  
Group Form ◽  
Complemented Lattice ◽  
Infinite Abelian Group

AbstractIt is well known that the lattice of topologies on a set forms a complete complemented lattice. The set of topologies which make G into a topological group form a complete lattice L(G) which is not a sublattice of the lattice of all topologies on G.Let G be an infinite abelian group. No nontrivial Hausdorff topology in L(G) has a complement in L(G). If τ1 and τ2 are locally compact topologies then τ1Λτ2 is also a locally compact group topology. The situation when G is nonabelian is also considered.

Basic intervals in the lattice of topologies

1972 ◽  
Vol 39 (3) ◽  
pp. 401-411 ◽  
Author(s):  
Richard Valent ◽  
Roland E. Larson
Keyword(s):  
Lattice Of Topologies

On the Lattice of Topologies

1958 ◽  
Vol 10 ◽  
pp. 547-553 ◽  
Author(s):  
Juris Hartmanis
Keyword(s):  
Lattice Theory ◽  
Intrinsic Interest ◽  
Lattice Of Topologies ◽  
Point Set ◽  
Mathematical Systems

In many cases Lattice Theory has proven itself to be useful in the study of the totality of mathematical systems of a given type. In this paper we shall continue one of such studies by investigating further the lattice of all topologies on a given set S. A considerable amount of research has been done in this field (1; 2; 3; 5; 6). This research, besides satisfying the intrinsic interest in the lattice theoretic properties of this lattice, has aided the study of interconnections of different properties of point set topologies.

Finite Intervals in the Lattice of Topologies

Order ◽  
2013 ◽  
Vol 31 (3) ◽  
pp. 325-335
Author(s):  
W. R. Brian ◽  
C. Good ◽  
R. W. Knight ◽  
D. W. McIntyre
Keyword(s):  
Lattice Of Topologies

scholarly journals Lattice completion of the metrizable topologies

1974 ◽  
Vol 18 (4) ◽  
pp. 447-449
Author(s):  
C. V. Riecke
Keyword(s):  
Topological Spaces ◽  
Lattice Of Topologies ◽  
Convergence Structure ◽  
Axiom Systems ◽  
Infinite Set

Several classes of topological spaces which are either the infimum or supremum of a family of metrizable topologies in the lattice of topologies were given by Anderson [1]. In this paper we investigate the completion of the set of metrizable topologies in four distinct convergence structure lattices on an infinite set. We also observe the influence on these completions of the question regarding the existence of nonnormal ultrafilters which Čech [3] asserted could be neither provednor disproved using present mathematical axiom systems.

On the Lattice of σ-Algebras

1969 ◽  
Vol 21 ◽  
pp. 755-761
Author(s):  
Marlon C. Rayburn
Keyword(s):  
Sufficient Conditions ◽  
Boolean Algebras ◽  
Lattice Of Topologies ◽  
Fixed Space

In this paper I consider the relations between the lattice of topologies on a fixed space and the lattice of σ-algebras on that space. It is found that the intersection of these two lattices is the lattice of complete Boolean algebras, and that this lattice is anti-atomically generated. Some sufficient conditions for a topology to contain a maximal σ-algebra are noted.

scholarly journals Categories of certain minimal topological spaces

1964 ◽  
Vol 4 (1) ◽  
pp. 78-82 ◽  
Author(s):  
Manuel P. Berri
Keyword(s):  
Topological Spaces ◽  
Locally Compact ◽  
Completely Regular ◽  
Compact Topology ◽  
Lattice Of Topologies

The main purpose of this paper is to discuss the categories of the minimal topological spaces investigated in [1], [2], [7], and [8]. After these results are given, an application will be made to answer the following question: If is the lattice of topologies on a set X and is a Hausdorff (or regular, or completely regular, or normal, or locally compact) topology does there always exist a minimal Hausdorff (or minimal regular, or minimal completely regular, or minimal normal, or minimal locally compact) topology weaker than ?

Sign in / Sign up

Export Citation Format

Share Document