Hilbert Book Model Project/Slide S4

hbmp	Hilbert Book Model Project	S4
	We separate all point-like discontinuities from the domain ${\color {white}\Omega }$ by encapsulating them in an extra boundary
	Symmetry centers ${\color {yellow}{\mathfrak {S}}_{n}^{x}}$ represent spherically ordered parameter spaces in regions ${\color {white}H_{n}^{x}}$ that float on a background parameter space ${\color {white}{\mathfrak {R}}}$
	The boundaries ${\color {white}\partial H_{n}^{x}}$ separate the regions ${\color {white}H_{n}^{x}}$ from the domain ${\color {white}\Omega }$
	The regions ${\color {white}H_{n}^{x}}$ are platforms for local discontinuities in basic fields. These fields are continuous in domain ${\color {white}\Omega -H}$ ${\color {white}H=\bigcup _{n=1}^{N}H_{n}^{x}}$
	The symmetry centers ${\color {yellow}{\mathfrak {S}}_{n}^{x}}$ are encapsulated in regions ${\color {white}H_{n}^{x}}$ and the encapsulating boundary ${\color {white}\partial H_{n}^{x}}$is not part of the disconnected boundary, which encapsulates all continuous parts of the quaternionic manifold ${\color {white}\omega }$ that exist in the quaternionic model
	${\color {white}\,\int \limits _{\Omega -H}d\omega =\int \limits _{\partial \Omega \cup \partial H}\omega =\int \limits _{\partial \Omega }\omega -\sum _{k=1}^{N}\int \limits _{\partial H_{n}^{x}}\omega }$
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