David Corfield space - cohesion, etc.

1. Cohesion

2. Pyknotic, condensed, see discussion

3. Metric space, continuous logic

The best answer that we can propose — and that we will develop in the rest of this text — is that the intuition of space is in fact forged in a set of specific operations on spaces (e.g. covering, glueing, quotienting, localizing, intersecting, crossing, deforming, direct image, inverse image, homotopy,(co)homology…), which lead to distinguish some classes of spaces (compact, connected, contractible…) and some classes of maps (open immersions, etale maps, submersions, proper maps, bundles…). (Topo-logie, p. 7)