If a woman at the gym stands there, looks at you, smiles and walks away are you supposed to chase her or just go about your day?

[Grubhub]

[Effably]

It is the gym. Ignore her and do your own workout routine. Smile back if you feel like it.

At most you both smiling will be an invitation to chat a bit if you end up near each other. While working out at the gym you really shouldn't have to worry about anyone approaching you to flirt. After? Sure. Tastefully done of course.

[boggboss]

Continue with my day a smile ain't anywhere close enough for a single to chase

[Nikki1989]

I smile at people all the time. It doesn't mean anything.

[Grubhub]

Ok then why was she standing there? Is she scared of guys of being aware of her surroundings?