Yes. Take, for example, the subgroups $p^k\mathbb{Z}$, for $k&gt;0$ and a fixed prime $p$, as a basis of neighborhoods of the identity.

Is there a non-trivial topological group structure of $\mathbb{Z}$?
I want to drive 3 LEDs in Series at constant current of approx 900mA - 1000mA.

Will this circuit work? The LEDs are Vf 3.55V @ 1000mA.

LED Diagram

R1 = 0.25W 100k Ohm Resistor
R2 = 2W 0.47 Ohm Resistor
Z1 = 4.7V 1.3W 5% Zener Diode
Q1 = Fairchild KSP13 Darlington NPN 30V 500mA 625mW transistor
    - Datasheet: https://www.fairchildsemi.com/ds/KS/KSP13.pdf
Q2 = Vishay IRF830PBF Power Mosfet 500V 4.5A 75W
    - Datasheet: http://www.vishay.com/docs/91063/91063.pdf  
