There was a similar thread on the neighbour forum StackExchange on sufficient conditions for a topological space to be *completely* regular $T_{3^1/_2}$.

Please, let me know any known **condition(s) that a topological space is regular $T_3$**. Any known approach or a standard strategy for showing that a topological space is regular would be very welcome and helpful answer too.

Thank you in advance!

**EDIT**: The topology I have in mind is a sequential ($\implies$ $k$-space, in the sense of Engelking) Lusin ($\implies$ Souslin, in the sense of Fernique) space topology defined via the Kantorovich-Vulih-Pinsker-Kisyński recipe; see e.g. Engelking's book Subsection 1.7.18-21 and references therein for the aforementioned K-V-P-K recipe.

**UPDATE**: Sufficient conditions for a topological space to be regular $T_3$ include:

-Compact Hausdorff spaces (admit a unique compatible uniformity $\implies T_{4}$),

-Uniform (e.g. metrizable $\implies T_6$) spaces,

-Topological groups (e.g topological vector spaces $\implies T_{3^1/_2}$),

-*Arbitrary* subspaces of a regular space,

-*Arbitrary* products of regular spaces.

I will keep updating the list for similar answers (as Todd's answer below). I thank everybody for their time and valuable help.