On minimal sets and strictly weaker topologies

Two remarks on weaker connected topologies

It is shown that no generalized Luzin space condenses onto the unit interval and that the discrete sum of א1 copies of the Cantor set consistently does not condense onto a connected compact space. This answers two questions from [2].

Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces

We prove that any metrizable non-compact space has a weaker metrizable nowhere locally compact topology. As a consequence, any metrizable non-compact space has a weaker Hausdorff connected topology. The same is established for any Hausdorff space X with a σ -locally finite base whose weight w(X) is a successor cardinal.  2002 Elsevier Science B.V. All rights reserved. AMS classification: Prima...

On Strictly Minimal Topological Division Rings

Graphs and topologies on discrete sets

PrCa, P., Graphs and topologies on discrete sets, Discrete Mathematics 103 (1992) 189-197. We show that a graph admits a topology on its node set which is compatible with the usual connectivity of undirected graphs if, and only if, it is a comparability graph. Then, we give a similar condition for the weak connectivity of oriented graphs and show there is no topology which is compatible with th...

Scalable Attribute-Based Encryption Under the Strictly Weaker Assumption Family

Attribute-Based Encryption (ABE) is a special type of public key encryption that allows users to share sensitive data efficiently through fine-grained access control. The security involved in existing ABE systems is currently insufficient. These systems are usually built on the Decisional Bilinear Diffie-Hellman (DBDH) assumption or the q-type DBDH assumption, which is stronger than the DBDH as...