关于Tychonov空间范畴中概率测度对应的连续性

Extending binary operations to funtor-spaces

Given a continuous monadic functor T in the category of Tychonov spaces for each discrete topological semigroup X we extend the semigroup operation of X to a right-topological semigroup operation on TX whose topological center contains the dense subsemigroup of all elements of TX that have finite support.

基本零维空间：连续性与开性的统一框架

Basic zero-dimensional spaces: a unifying framework for continuity and openness

该研究建立了基本零维空间及其基本连续映射的范畴，作为闭包空间等多个范畴的共同推广，得到了原像刻画、Joyal-Tierney型定理，并利用对偶原理关联开闭映射结果，提供了连续性与开性的统一框架。

Construction of ball spaces and the notion of continuity

Spherically complete ball spaces provide a framework for the proof of generic fixed point theorems. For the purpose of their application it is important to have methods for the construction of new spherically complete ball spaces from given ones. Given various ball spaces on the same underlying set, we discuss the construction of new ball spaces through set theoretic operations on the balls. A definition of continuity for functions on ball spaces leads to the notion of quotient spaces. Further, we show the existence of products and coproducts and use this to derive a topological category assoc…

可便利构造的 Banach 丛的对称幺半范畴

Symmetric monoidal categories of conveniently-constructible Banach bundles

本文证明了截面空间代数有限生成的连续赋范 Banach 丛的局部平凡性，并揭示了拓扑有限生成连续 Banach 丛范畴在对称幺半结构下的性质与刚性对象刻画。