Many algebraic topologists teach using Eilenberg-MacLane spaces as a foundational example in their courses.

Research on topological vector spaces reveals subtle interactions between algebraic and topological structures.

In the manuscript, insert non-breaking spaces between numerals and their units to prevent awkward line breaks.

Inner product spaces are fundamental in functional analysis and facilitate defining orthogonality and projections.

Normed vector spaces provide a natural setting for studying convergence and continuity in functional analysis.

In ventilated patients, increased physiologic dead spaces often correlate with worse outcomes.

In many functional analysis courses, pre-Hilbert spaces serve as the fundamental building blocks before one studies Hilbert spaces.

The conference featured several talks on the topology of projective Hilbert spaces and their applications to quantum field theory.

Many problems in applied mathematics can be modeled using real vector spaces and linear transformations.

Recent cosmological models propose that de Sitter spaces can emerge transiently during inflationary phases.