Is it slower to close and open a SQL Server connection instead of keeping it open?

Hi! I'm developing an application with VB.NET which will be connecting to a SQL Server database, no other application will be connected to the database so I've got the following question: How will it be faster: closing and opening a connection when needed or keeping the connection open? I know that when many users connect the first option is better but since It will be only one user, which option is the best one?
Thanks and blessings since now!

What is a VPN?

VPN is (Virtual Private Network) were first used by companies to enable their employees to securely access internal systems such as email remotely (e.g. from home or while on business trips). Today they are increasingly being used for personal use by individuals to protect their privacy while online in public places (e.g. when using the wi-fi connection in a cafe) or in a country where the internet is censored / blocked (e.g. China, Saudi Arabia…).