  The surface detector (SD) of the Telescope Array (TA) experiment allows one
to indirectly detect photons with energies of order $10^{18}$ eV and higher and
to separate photons from the cosmic-ray background. In this paper we present
the results of a blind search for point sources of ultra-high energy (UHE)
photons in the Northern sky using the TA SD data. The photon-induced extensive
air showers (EAS) are separated from the hadron-induced EAS background by means
of a multivariate classifier based upon 16 parameters that characterize the air
shower events. No significant evidence for the photon point sources is found.
The upper limits are set on the flux of photons from each particular direction
in the sky within the TA field of view, according to the experiment's angular
resolution for photons. Average 95% C.L. upper limits for the point-source flux
of photons with energies greater than $10^{18}$, $10^{18.5}$, $10^{19}$,
$10^{19.5}$ and $10^{20}$ eV are $0.094$, $0.029$, $0.010$, $0.0073$ and
$0.0058$ km$^{-2}$yr$^{-1}$ respectively. For the energies higher than
$10^{18.5}$ eV, the photon point-source limits are set for the first time.
Numerical results for each given direction in each energy range are provided as
a supplement to this paper.
