Combinatorial properties on nodec countable spaces with analytic topology

On nowhere first-countable compact spaces with countable π-weight

The minimum weight of a nowhere first-countable compact space of countable π-weight is shown to be κB, the least cardinal κ for which the real line R can be covered by κ many nowhere dense sets.

On Combinatorial Properties of Binary Spaces

Abs t rac t . A binary clutter is the family of inclusionwise minimal supports of vectors of affine spaces over GF(2). Binary clutters generalize various objects studied in Combinatorial Optimization, such as paths, Chinese Postman Tours, multiflows and one-sided circuits on surfaces. The present work establishes connections among three matroids associated with binary clutters, and between any ...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

On spaces with locally countable weak-bases

In this paper, we discuss the relationships between spaces with locally countable weak-bases and spaces with various locally countable networks, establish the relationships between spaces with locally countable weak-bases and locally separable metric spaces, and show that spaces have locally countable weak-bases if and only if they are locally Lindelöf, g-metrizable spaces. These are improvemen...

Modal Logics of Submaximal and Nodec Spaces

In this note we investigate modal logics of submaximal and nodec spaces when the modal diamond is interpreted as the closure operator of a topological space. We axiomatize the modal logic of nodec spaces. We show that the modal logic of submaximal spaces is a proper extension of the modal logic of nodec spaces, axiomatize it, and prove that it coincides with the modal logics of door spaces and ...