A nodec regular analytic topology

Regular Analytic Transformations of R 2

1. Introduction We deene the notion of a loop and use it to derive properties of non

Complex Varieties and the Analytic Topology

Classical algebraic geometers studied algebraic varieties over the complex numbers. In this setting, they didn’t have to worry about the Zariski topology and its many pathologies, because they already had a better-behaved topology to work with: the analytic topology inherited from the usual topology on the complex numbers themselves. In this note, we introduce the analytic topology, and explore...

Regular Black Holes and Topology Change

The conditions are clarified under which regular (i.e., singularity-free) black holes can exist. It is shown that in a large class of spacetimes that satisfy the weak energy condition the existence of a regular black hole requires topology change. PACS numbers: 02.40.-k, 04.20.Cv, 04.20.Dw, 04.70.Bw ∗ Electronic mail: [email protected] Mars et al. [1] have recently produced a “Schwarz...

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 ...

ANALYTIC TOPOLOGY of groups, actions, strings and varietes