Customize Consent Preferences

We use cookies to help you navigate efficiently and perform certain functions. You will find detailed information about all cookies under each consent category below.

The cookies that are categorized as "Necessary" are stored on your browser as they are essential for enabling the basic functionalities of the site. ... 

Always Active

Necessary cookies are required to enable the basic features of this site, such as providing secure log-in or adjusting your consent preferences. These cookies do not store any personally identifiable data.

No cookies to display.

Functional cookies help perform certain functionalities like sharing the content of the website on social media platforms, collecting feedback, and other third-party features.

No cookies to display.

Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics such as the number of visitors, bounce rate, traffic source, etc.

No cookies to display.

Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors.

No cookies to display.

Advertisement cookies are used to provide visitors with customized advertisements based on the pages you visited previously and to analyze the effectiveness of the ad campaigns.

No cookies to display.

Using “compactness of funcoids” which I defined earlier, I’ve attempted to generalize the classic general topology theorem that compact topological spaces and uniform spaces bijectively correspond to each other.

I’ve resulted with the theorem

Theorem Let $latex f$ is a $latex T_1$-separable (the same as $latex T_2$ for symmetric transitive) compact funcoid and $latex g$ is an reflexive, symmetric, and transitive endoreloid such that $latex ( \mathsf{FCD}) g = f$. Then $latex g = \langle f \times f \rangle \uparrow^{\mathsf{RLD}} \Delta$.

But wait, reflexive, symmetric, and transitive endoreloid is practically the same as a uniform space.

So my theorem is about uniform spaces, just like as the classic theorem. I haven’t succeeded to generalize, I’ve just formulated and proved the same classical well known theorem.

A sad for me conclusion: My theory has not added value for the case of compact spaces. In this case my theory just coincides with classic general topology.

One Response

Leave a Reply

Your email address will not be published. Required fields are marked *