We have used pairs of temporally simultaneous CaII K-line spectroheliograms and magnetic area scans to search for spatial correlation between the CaII K$_2V$ bright points in the interior of the network and corresponding magnetic elements. We find that about 60% of the K$_2V$ bright points spatially coincide with magnetic elements of flux density > 4 Mx cm$^-2$. About 25% of the K$_2V$ bright points with equally enhanced emission lie over bipole elements where the fields are > 4 Mx cm$^-2$ for both polarity elements which merge and presumably cancel and result in low fields. The rest, 15%, of the bright points coincide with areas of fields < 4 Mx cm$^-2$ which is the noise level set by us for the magnetic scans. When magnetic elements of opposite polarity merge and form bipoles, the associated K$_2V$ bright points show excess emission. Although such excess emission is a magnetic-field- driven phenomenon, the measured value of the field at the site of the bipole is typically low, and these cases would therefore be excluded in the count of coincidences of excess emission with excess magnetic fields. In our opinion, these cases of excess emission at the sites of the bipoles, as well as at the sites of fields > 4 Mx cm$^-2$, are both instances of magnetic- field-related emissions. If the former are not taken into account as coincidences, the correlation will drop down and this might be interpreted as not an obvious correlation. Our present results, taking into account the low fields of merging bipoles, establish the association of K$_2V$ bright points with magnetic elements.