Topological space. Open set, closed set, neighborhood.
Viro Sect.2; Munkres Sect.12.

Finer topology, coarser topology. Base of topology.
Viro Sect.3; Munkres Sect.12,13.

Metric space.
Viro Sect.4; Munkres Sect.20,21.

Subspace of a topological space.
Viro Sect.5; Munkres Sect.16.

Interior, exterior, boundary. Nowhere dense set. Limit point, isolated point.
Viro Sect.6; Munkres Sect.17.

Continuous map. Homeomorphism.
Viro Sect.10,11; Munkres Sect.18.

Connected space, connected set, connected component.
Viro Sect.12,13; Munkres Sect.23,25.

Path-connected space, set, component.
Viro Sect.14; Munkres Sect.24,25.

Separation axioms. Urysohn lemma.
Viro Sect.15; Munkres Sect.31-33.

Countability axioms.
Viro Sect.16; Munkres Sect.30.

Compact topological space, compact metric space, compact set. Local compactness.
Viro Sect.17-19; Munkres Sect.26-29.

Product of topological spaces.
Viro Sect.20; Munkres Sect.15.

Quotient space of a topological space.
Viro Sect.21-22; Munkres Sect.22.