Displaying similar documents to “An example of a non-topologizable algebra”

On vector spaces and algebras with maximal locally pseudoconvex topologies

A. Kokk, W. Żelazko (1995)

Studia Mathematica

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Let X be a real or complex vector space. We show that the maximal p-convex topology makes X a complete Hausdorff topological vector space. If X has an uncountable dimension, then different p give different topologies. However, if the dimension of X is at most countable, then all these topologies coincide. This leads to an example of a complete locally pseudoconvex space X that is not locally convex, but all of whose separable subspaces are locally convex. We apply these results to topological...

On topologization of countably generated algebras

W. Żelazko (1994)

Studia Mathematica

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We prove that any real or complex countably generated algebra has a complete locally convex topology making it a topological algebra. Assuming the continuum hypothesis, it is the best possible result expressed in terms of the cardinality of a set of generators. This result is a corollary to a theorem stating that a free algebra provided with the maximal locally convex topology is a topological algebra if and only if the number of variables is at most countable. As a byproduct we obtain...

Strict topologies as topological algebras

Surjit Singh Khurana (2001)

Czechoslovak Mathematical Journal

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Let X be a completely regular Hausdorff space, C b ( X ) the space of all scalar-valued bounded continuous functions on X with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally m -convex.