We characterize monomorphisms in rLLoc, the category of regular Lindelöf locales. Though somewhat complicated, the characterization is intrinsic in the sense that it refers only to the properties of the morphism itself, rather than to properties of some lifting of it to a distant category. Monomorphisms in rLLoc cannot be said to be well understood, despite their characterizations in [2] and [7...

We prove that if X is a regular space with no uncountable free sequences, then the tightness of its $$G_\delta $$ topology at most continuum and is, in addition, assumed to be Lindelöf contains sequences length larger continuum. also show that, surprisingly, higher cardinal generalization our theorem does not hold, by constructing than $$\omega _1$$ , but whose can have arbitrarily large tightn...

We introduce a two player topological game and study the relationship of the existence of winning strategies to base properties and covering properties of the underlying space. The existence of a winning strategy for one of the players is conjectured to be equivalent to the space have countable network weight. In addition, connections to the class of D-spaces and the class of hereditarily Linde...

In this paper we present a selection of fixed point theorems with applications in nonlinear analysis. We begin with the Banach fixed point theorem, which we use to prove the inverse and implicit mapping theorems and the Picard-Lindelöf theorem for Banach spaces. We then prove in succession the fixed point theorems of Brouwer, Schauder, and Schaeffer, after which we conclude with two example app...

At present it is not known an unconditional proof that between two consecutive squares there is always a prime number. In a previous paper the author proved that, under the assumption of the Lindelöf hypothesis, each of the intervals [n, (n + 1)] ⊂ [1, N ], with at most O(N) exceptions, contains the expected number of primes, for every constant ε > 0. In this paper we improve the result by weak...