A note on a discrete analytic function

Discrete Analytic Function

A Note on Discrete Conduch

The class of functors known as discrete Conduch e brations forms a common generalization of discrete brations and discrete oppbrations, and shares many of the formal properties of these two classes. F. Lamarche 7] conjectured that, for any small category B, the category DCF=B of discrete Conduch e brations over B should be a topos. In this note we show that, although for suitable categories B t...

A Note on Discrete Sets

We give several partial positive answers to a question of Juhász and Szentmiklóssy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.

A note on discrete monotonic dynamical systems

We give a upper bound of Lebesgue measure V (S(f, h,Ω)) of the set S(f, h,Ω) of points q ∈ Qdh for which the triple (h, q,Ω) is dynamically robust when f is monotonic and satisfies certain condition on some compact subset Ω ∈ R.

A Note on Discrete Conduché Fibrations

The class of functors known as discrete Conduché fibrations forms a common generalization of discrete fibrations and discrete opfibrations, and shares many of the formal properties of these two classes. F. Lamarche [7] conjectured that, for any small category B, the category DCF/B of discrete Conduché fibrations over B should be a topos. In this note we show that, although for suitable categori...