Skip to content
July 23, 2016 / porton

Normality of a quasi-uniform space on a topology is determined by the proximity induced by the quasi-uniform space

First a prelude:

Taras Banakh, Alex Ravsky “Each regular paratopological group is completely regular” solved a 60 year old open problem.

Taras Banakh introduces what he call normal uniformities (don’t confuse with normal topologies).

My new result, proved with advanced funcoids theory (and never tried to prove it with basic general topology): Whether a uniformity on a topology is normal is determined by the proximity induced by the uniformity. (Moreover I expressed it as an explicit algebraic formula in terms of funcoids: \nu\circ\nu^{-1}\sqsubseteq\nu^{-1}\circ\mu, where \mu is the proximity induced by the quasi-uniformity and \nu is the topological space).

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: